Synthesis of Large-Grained Polycrystalli

Synthesis of Large-Grained Polycrystalline Silicon by Hot-Wire Chemical Vapor Deposition for Thin Film Photovoltaic Applications - CaltechTHESIS
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Synthesis of Large-Grained Polycrystalline Silicon by Hot-Wire Chemical Vapor Deposition for Thin Film Photovoltaic Applications
Citation
Mason, Maribeth Swiatek
(2004)
Synthesis of Large-Grained Polycrystalline Silicon by Hot-Wire Chemical Vapor Deposition for Thin Film Photovoltaic Applications.
Dissertation (Ph.D.), California Institute of Technology.
doi:10.7907/7K9R-VX22.
Abstract
In this study, we investigate the fabrication of large-grained polycrystalline silicon by hot-wire chemical vapor deposition (HWCVD) and its suitability for thin-film photovoltaic applications. We have devised two strategies for the fast, low-temperature growth of thin polycrystalline silicon films on glass substrates. The first is the direct growth of polycrystalline silicon on SiO₂ by HWCVD. We use atomic force microscopy (AFM) to characterize fully continuous polycrystalline silicon films grown by HWCVD on SiO₂, as well as the nucleation density of silicon islands formed in the early stages of HWCVD growth, as a function of temperature and hydrogen dilution (H₂:SiH₄). Our observations of the nucleation kinetics of Si on SiO₂ can be explained by a rate-equation pair-binding model, from which we derive an estimate for the prefactor and activation energy for surface diffusion of Si on SiO₂ during HWCVD growth and assess the viability of this method for the rapid growth of large-grained polycrystalline silicon on SiO₂.
The second strategy uses large-grained (~100 µm) polycrystalline silicon layers fabricated by selective nucleation and solid-phase epitaxy (SNSPE) on SiO₂ substrates as templates for epitaxial growth by HWCVD. Using reflection high-energy electron diffraction (RHEED) and transmission electron microscopy (TEM), we have derived a phase diagram for Si on Si(100) consisting of epitaxial, twinned epitaxial, mixed epitaxial/polycrystalline, and polycrystalline phases of growth on Si(100) in the 50 nm-2 µm thickness regime. Evidence is also presented for epitaxial growth on SNSPE templates, which use nickel nanoparticles as nucleation sites for the solid-phase crystallization of phosphorus-doped amorphous silicon on SiO₂. Minority carrier lifetimes for films on Si(100), as measured by resonant-coupled photoconductive decay experiments, range from 5.7 to 14.8 microseconds while those for films on SNSPE templates range from 5.9 to 19.3 microseconds. Residual nickel present in the SNSPE templates does not significantly affect the lifetime of films grown on SNSPE templates, making the growth of epitaxial layers by HWCVD on SNSPE templates a possible strategy for the fabrication of thin-film photovoltaics.
Item Type:
Thesis (Dissertation (Ph.D.))
Subject Keywords:
cat-CVD; hot-wire CVD; photovoltaics; solar cells
Degree Grantor:
California Institute of Technology
Division:
Engineering and Applied Science
Major Option:
Applied Physics
Thesis Availability:
Public (worldwide access)
Research Advisor(s):
Atwater, Harry Albert
Thesis Committee:
Atwater, Harry Albert (chair)
Bockrath, Marc William
Flagan, Richard C.
Haile, Sossina M.
Goddard, William A., III
Defense Date:
14 January 2004
Record Number:
CaltechETD:etd-03182004-221215
Persistent URL:
DOI:
10.7907/7K9R-VX22
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No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:
998
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CaltechTHESIS
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Deposited On:
22 Mar 2004
Last Modified:
08 Nov 2023 00:12
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Synthesis of Large-Grained Polycrystalline Silicon by
Hot-Wire Chemical Vapor Deposition for Thin Film
Photovoltaic Applications

Thesis by

Maribeth Swiatek Mason

In Partial Fulfillment of the Requirements
for the Degree of
Doctor of Philosophy

California Institute of Technology
Pasadena, California

2004
(Submitted January 14, 2004)

2004

Maribeth Swiatek Mason

iii

Acknowledgements
After a number of misadventures, I’ve finally been tapped by the Blue Fairy to become a Real
Scientist. My success in this endeavor is largely a result of being lucky enough to meet the right
people, each of whom gave me something useful to help me along the journey. I hope that I have
given each of them something useful in return.
For direct contributions to the content of this thesis, I am grateful to Carol Garland, a model
of true kindness and patience, who helped perform TEM analysis; Dick Ahrenkiel, who performed
RCPCD lifetime measurements; Eric Schiff and Steluta Dinca, who performed time-of-flight mobility measurements; Matt Dicken, who performed RHEED measurements; John Venables, with
whom I engaged in valuable discussions of nucleation kinetics; and Richard Mason, who helped with
MATLAB and Mathematica syntax.
A fortuitous choice of desk in 1997 gave me the Best Officemates Ever, who shared in the joys
of Good Science Days and made even the worst of Bad Science Days a little brighter. Many thanks
to Julie Biteen, who mailed my samples, checked out library books for me, and provided wise
advice on grammar and everything else; Luke Sweatlock, who crimped, hammered and tightened
most of the parts on the HWCVD reactor and gave me a good reason to take up the piano again;
Christine Richardson, who provided SNSPE templates and introduced me to the joys of Paradise
Hotel; Claudine Chen, who taught me the art of TEM and SNSPE and generously gave good counsel
and true friendship; Jason Holt, who made it almost as much fun to build that wretched manipulator
as it was to spend the generous Denver-area per diem; and Jimmy Zahler (who really should just
move in to 244 for all the time he spends gossiping in there), who helped me “change the tone”
when science made me grumpy.
I am privileged to have been a member of the Atwater group, who continually gave me support,
fun and friendship. For this I thank (in no particular order) Julie Casperson, Tao Feng, Pieter
Kik, Mark Brongersma, Albert Polman, David Boyd, Robb Walters, Jen Ruglovsky, Rhett Brewer,
Stefan Maier, Kyu Min, Liz Boer, Regina Ragan, Cecily Ryan, Matt Norman, Anna Fontcuberta i
Morral, John Hartman, Torsten Bistritschan, Brendan Kayes, Young-Bae Park, Aditi Risbud, Katsu
Tanabe, Beth Lachut and Jen Dionne.
Throughout my studies I was fortunate to find the best of mentors. Each of them had so many

iv
good qualities which I wish to emulate in my career, and I hope to honor them with my future
success. Many years ago, Mark Kirk told me I would make a good scientist, which still keeps me
going when things seem impossible. John Abelson’s ongoing help, kindness and encouragement
have been priceless; it’s thanks to his efforts I began this at all. Finally, I have been inspired by
the creative vision of Harry Atwater. I will always be thankful that he did not make me move to
Harvard, and more importantly, that he never gave up on me even through my worst failures.
I am of course forever grateful to my family, who trusted me to seek my fortune in California
and always said they would still love me even if I quit my Ph.D. Finally, thanks to my dearest
love, Richard, who from the beginning carried me, sometimes kicking and screaming, through this
experience. He’s right, as usual – I’m happy I found the strength to finish this, and I hope I’ve made
him proud.

Abstract
In this study, we investigate the fabrication of large-grained polycrystalline silicon by hot-wire chemical vapor deposition (HWCVD) and its suitability for thin-film photovoltaic applications. We have
devised two strategies for the fast, low-temperature growth of thin polycrystalline silicon films on
glass substrates. The first is the direct growth of polycrystalline silicon on SiO2 by HWCVD. We use
atomic force microscopy (AFM) to characterize fully continuous polycrystalline silicon films grown
by HWCVD on SiO2 , as well as the nucleation density of silicon islands formed in the early stages of
HWCVD growth, as a function of temperature and hydrogen dilution (H2 :SiH4 ). Our observations
of the nucleation kinetics of Si on SiO2 can be explained by a rate-equation pair-binding model,
from which we derive an estimate for the prefactor and activation energy for surface diffusion of
Si on SiO2 during HWCVD growth and assess the viability of this method for the rapid growth of
large-grained polycrystalline silicon on SiO2 .
The second strategy uses large-grained (∼100 µm) polycrystalline silicon layers fabricated by
selective nucleation and solid-phase epitaxy (SNSPE) on SiO2 substrates as templates for epitaxial
growth by HWCVD. Using reflection high-energy electron diffraction (RHEED) and transmission
electron microscopy (TEM), we have derived a phase diagram for Si on Si(100) consisting of epitaxial,
twinned epitaxial, mixed epitaxial/polycrystalline, and polycrystalline phases of growth on Si(100)
in the 50 nm–2 µm thickness regime. Evidence is also presented for epitaxial growth on SNSPE
templates, which use nickel nanoparticles as nucleation sites for the solid-phase crystallization of
phosphorus-doped amorphous silicon on SiO2 . Minority carrier lifetimes for films on Si(100), as
measured by resonant-coupled photoconductive decay experiments, range from 5.7 to 14.8 µs while
those for films on SNSPE templates range from 5.9 to 19.3 µs. Residual nickel present in the SNSPE
templates does not significantly affect the lifetime of films grown on SNSPE templates, making the
growth of epitaxial layers by HWCVD on SNSPE templates a possible strategy for the fabrication
of thin-film photovoltaics.

Contents
Acknowledgements

iii

Abstract

1 Introduction

1.1

Photovoltaics as a renewable energy source . . . . . . . . . . . . . . . . . . . . . . .

1.2

Photovoltaics past . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1.3

Photovoltaics present—current technology . . . . . . . . . . . . . . . . . . . . . . . .

1.3.1

Device operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1.3.2

Materials for photovoltaics . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1.3.3

Crystalline silicon technologies . . . . . . . . . . . . . . . . . . . . . . . . . .

Photovoltaics future—thin-film polycrystalline silicon? . . . . . . . . . . . . . . . . .

1.4

2 Hot-Wire Chemical Vapor Deposition

2.1

Advantages for thin-film photovoltaics . . . . . . . . . . . . . . . . . . . . . . . . . .

2.2

Development of HWCVD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.3

Recent work in HWCVD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.4

Thin-film HWCVD-deposited solar cells . . . . . . . . . . . . . . . . . . . . . . . . .

2.5

Outline of the thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3 Nucleation on SiO2

3.1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.2

Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.3

Quantitative modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.4

Microstructural control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.5

Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4 Epitaxial Growth by HWCVD

4.1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.2

Low-temperature epitaxy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

vii
4.3

Epitaxy on Si (100) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.3.1

Initial experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.3.1.1

Growth conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.3.1.2

Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Further experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.3.2.1

Growth conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.3.2.2

Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Epitaxy on large-grained polycrystalline templates . . . . . . . . . . . . . . . . . . .

4.4.1

Selective nucleation and solid phase epitaxy . . . . . . . . . . . . . . . . . . .

4.4.2

Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.3.2

4.3.3
4.4

4.5

5 Minority Carrier Lifetimes of HWCVD Films

5.1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5.2

Recombination in semiconductors . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5.3

Resonant-coupled photoconductive decay . . . . . . . . . . . . . . . . . . . . . . . .

5.4

Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5.5

Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5.6

Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6 Conclusions and Future Work

Bibliography

A The HWCVD Reactor

B Nucleation Model Code

C Hydrogen Surface Coverage Model Code

viii

List of Figures
1.1

(a) Energy spectrum of solar radiation. The large absorption peaks are due mainly
to water and CO2 in the atmosphere. (b) Ideal cell efficiency as a function of band
gap energy, assuming no losses. The band gaps of several semiconductors used in
photovoltaics are labeled. [1] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.1

Schematic of the HWCVD process. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.2

Number of papers on HWCVD published since its introduction in 1979. Matsumura
resurrected the technique in 1986. The First International Conference on Cat-CVD
(Hot-Wire CVD) was held in 2000, with the Second International Conference following
in 2002. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.1

Schematic of hot-wire CVD experiments. . . . . . . . . . . . . . . . . . . . . . . . . .

3.2

Net deposition rate and SiH4 mole fraction as a function of H2 partial pressure in
100 mTorr of dilute SiH4 1% in He. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.3

(a)AFM of the HWCVD nucleation phase. This image was taken after a growth time
of 90 seconds at 20:1 H2 dilution. Bright features are ≥35 nm in height. (b) Postcoalescence 1 µm2 image of a continuous poly-Si film grown at zero H2 dilution; grain
size is 40 nm. (c) Post-coalescence 1 µm2 image of a continuous poly-Si film grown at
20:1 H2 dilution; grain size is 85 nm. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.4

Nucleation data as a function of H2 dilution at 300◦ C. The lines are a guide to the eye. 15

3.5

Temperature-dependent nucleation measurements. The lines are a guide to the eye.
The initial slope of the data were used to estimate the activation energy for surface
diffusion of Si on SiO2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.6

Comparison of simulated (lines) and experimental (dots) temperature-dependent cluster density measurements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.7

3.8

Comparison of simulated and experimental H2 dilution-dependent cluster density measurements at (a) 300◦ C and (b) 400◦ C. . . . . . . . . . . . . . . . . . . . . . . . . . .

Adatom stay time as a function of H2 dilution. . . . . . . . . . . . . . . . . . . . . . .

ix
3.9

Two-stage growth experiment, as compared to undiluted growth and growth at 60:1
H2 . The lines which fit the data at 0 H2 and 60:1 H2 are guides to the eye. . . . . . .

3.10

Pair-binding model simulations of growth at 60:1 H2 dilution, two-stage growth, and
ramped dilution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.1

Cross-sectional TEM of HWCVD-grown Si on Si (100) at 300◦ C. The epitaxial films
display a periodic array of stacking faults. . . . . . . . . . . . . . . . . . . . . . . . . .

4.2

(a) Cross-sectional TEM of HWCVD-grown Si on Si (100) at 300◦ C. The films become
highly twinned after a thickness of approximately 240 nm. Labels b, c, and d refer to
areas from which selected-area diffraction patterns were obtained. (b) Selected area
diffraction from HWCVD film and amorphous glue layer. (c) Selected area diffraction
from HWCVD film and Si (100) substrate. (d) Selected area diffraction from Si (100)
substrate. Higher-order spots in (b) and (c) are due to the periodic array of stacking
faults in the epitaxial film and twinning in the uppermost regions of the film. . . . . .

4.3

Cross-sectional TEM of HWCVD-grown Si on Si (100) at 400C , which displays mixed
epitaxial/polycrystalline growth. Hydrogen-induced defects are present in the substrate. 27

4.4

Cross-sectional TEM of 350 nm-thick film grown at 300◦ C. (a) 50 nm-thick epitaxial
layer before twinned growth begins. Inset: diffraction pattern from twinned region; (b)
Twinning continues throughout film growth. . . . . . . . . . . . . . . . . . . . . . . .

4.5

Cross-sectional TEM of 15 µm thick film grown at 300◦ C. (a) Stacking faults and twinning begin at interface. (b) Mixed twinned epitaxial/polycrystalline growth; twinned
regions extend as far as 300 nm into film. (c) Grain size of polycrystalline film is on
the order of 1 µm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.6

RHEED patterns of films of increasing thickness grown at 300 C. The beam is along
the <110> direction. Two phases of growth are observed: twinned epitaxial growth
[a-g] and polycrystalline growth [h]. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.7

4x4 µm AFM topography (top panels) and error mode (bottom panels) images of films
of increasing thickness grown at 300◦ C. . . . . . . . . . . . . . . . . . . . . . . . . . .

4.8

Phases of crystalline growth observable by RHEED. (a) 300◦ C, 60 nm thick twinned
epitaxial film. (b) 300◦ C, 330 nm thick twinned epitaxial film; increased surface roughness is responsible for the differences from (a). (c) 475◦ C, 60 nm thick film of mixed
phase; both spots (corresponding to twinned epitaxial growth) and rings (corresponding to polycrystalline growth) are evident. (d) 475◦ C, 330 nm thick polycrystalline

4.9

film. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Phase diagram of HWCVD films grown at 50:1 hydrogen dilution. . . . . . . . . . . .

4.10

Calculated equilibrium surface hydrogen coverages for HWCVD growth conditions
(H2 :SiH4 =50:1, 25 mTorr 4% SiH4 in He, wire 2.5 cm from substrate), with experimental temperature-programmed desorption data [2] for comparison. The shaded
area represents the temperature regime in which HWCVD growth experiments were
performed. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.11

Silicon to oxygen ratio in the first monolayer of growth as a function of dilution ratio
R (H2 /SiH4 at temperatures from 571 to 711 K. Pressure is held constant at 75 mTorr
of a gas mixture of H2 and 4% SiH4 in He. . . . . . . . . . . . . . . . . . . . . . . . .

4.12

Carbon, hydrogen, and oxygen concentrations in 2.2 µm thick film grown at 300 C, as
determined by SIMS analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.13

The SNSPE template fabrication process. . . . . . . . . . . . . . . . . . . . . . . . . .

4.14

Crystallization of SNSPE template layer [3]. The black dots are the nickel nanoparticles; the white areas are grains of crystalline silicon and the grey areas are amorphous
silicon regions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.15

Plan-view TEM of HWCVD epitaxial film (T=300 C) on SNSPE template. (a) Selected area diffraction pattern from underlying SNSPE template. (b) Selected area
diffraction pattern from HWCVD film on SNSPE template. (c) Bright-field image
indicating selected area diffraction regions. Inset: diffraction from entire area. . . . . .

4.16

(a) Bright-field image of HWCVD film (T=300◦ C) on SNSPE template showing selected area diffraction regions. (b) Selected area diffraction from HWCVD film on
(100)-oriented grain. (c) Selected area diffraction from HWCVD film on a grain of
different orientation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.17

(a) Bright-field image of HWCVD film (T=300◦ C) on SNSPE template showing selected area diffraction region. Inset: selected area diffraction pattern showing areas of
large-grained polcrystalline growth. (b) Dark-field image corresponding to region in
(a). (c) Bright-field image of 3.5 µm thick film with high intragranular defect density.

5.1
5.2

(d) Dark-field image corresponding to region in (b). . . . . . . . . . . . . . . . . . . .

Basic schematic of the RCPCD apparatus. . . . . . . . . . . . . . . . . . . . . . . . .

W concentration, as determined by SIMS analysis, in 300 C HWCVD silicon films
grown on Si(100) at wire temperatures of 1800◦ C and 1750◦ C. The higher W concentration at the surface of both films is due to exposure to the W wire before growth,
which was necessary to heat the samples to 300◦ C. . . . . . . . . . . . . . . . . . . . .

5.3

RCPCD voltage vs. time curves for HWCVD films of various thicknesses on Si(100).
(a) 1.5 µm, (b) 3.5 µm, (c) 11.5 µm, (d) 15 µm. Straight lines indicate exponential
decay fits to the data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

xi
5.4

RCPCD voltage vs time curves for HWCVD films of various thicknesses on SNSPE
templates. (a) 1.5 µm, (b) 3.5 µm, (c) 11.5 µm, (d) 15 µm. Straight lines indicate
exponential decay fits to the data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5.5

LLI and HLI minority carrier lifetimes of HWCVD films on Si(100) as measured by
RCPCD. The dashed and dotted lines represent the LLI and HLI lifetimes, respectively,
of the bulk Si(100) substrate. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5.6

LLI and HLI minority carrier lifetimes of HWCVD films on SNSPE templates as measured by RCPCD. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

A.1

Schematic of the HWCVD reactor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

A.2

Photographs of the HWCVD reactor. (a) Front view. (b) Side view. . . . . . . . . . .

A.3

Top view of the inside of the HWCVD reactor. The wire is on and is normal to the
plane of the photograph.

A.4

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Schematic of the inside of the HWCVD reactor during growth experiments. . . . . . .

xii

List of Tables
3.1

Coalescence times and grain densities of continuous films under various H2 dilution
conditions, as predicted by the pair-binding model. . . . . . . . . . . . . . . . . . . . .

4.1

Parameters used in hydrogen surface coverage model. . . . . . . . . . . . . . . . . . .

5.1

Reported electrical properties of intrinsic films. . . . . . . . . . . . . . . . . . . . . . .

Chapter 1

Introduction
1.1

Photovoltaics as a renewable energy source

The increasing costs of oil and natural gas and their dwindling supplies as world demand continues
to increase, as well as concerns over CO2 emissions and global warming, have led to increased efforts
in the development of renewable energy sources. One of the most promising techniques is the direct
conversion of solar energy into electricity through photovoltaic devices. Given a global average solar
irradiation of 1700 kWh/m2 /yr, solar energy is capable of producing 3×1024 J of energy each year [4].
By comparison, the global energy demand in the year 2000 was approximately 4×1020 J [5], making
it possible that, along with other alternative energy sources such as wind power and geothermal
energy, photovoltaics could be a solution to the energy crisis created by the eventual depletion of
fossil fuel reserves.

1.2

Photovoltaics past

The development of photovoltaics began in 1839, when Edmund Becquerel discovered that the
current through an electrolytic cell increased when exposed to light [6]. This result, along with
Willoughby Smith’s 1873 discovery of the photoconductivity of selenium, led to the first photovoltaic cell, fabricated by W. G. Adams and R. E. Day in 1877 [7]. Werner von Siemens called
the discovery“scientifically of the most far-reaching importance [8],” although these selenium cells
converted only one-tenth of one percent of the incident light into electricity.
It would be more than 75 years before Bell Laboratories scientist Gerald Pearson, while researching doping effects in silicon for electronics applications, accidentally fabricated a solar cell far more
efficient than the early selenium cells. In the spring of 1953, Pearson and his colleagues, Daryl Chapin
and Calvin Fuller, fabricated the first solar cell efficient enough to run electrical equipment [9]—a
discovery praised by the New York Times as “the beginning of a new era, leading eventually to the
realization of harnessing the almost limitless energy of the sun for the uses of civilization [10].”

Although U.S. News and World Report speculated that the silicon solar cells discovered at Bell
Laboratories would “provide more power than all the world’s coal, oil and uranium [11],” no applications of commercial significance immediately came to light. In fact, Chapin calculated that with
a one-watt cell costing $286 a homeowner would have to pay $1,430,000 for an array of sufficient
size to power the average American house. Solar cells doubled in efficiency in the ensuing eighteen
months, but companies such as Hoffmann Electronics, still desperate to find commercial outlets for
solar cells, only found them useful for powering toy boats and radios. However, Chapin’s colleague,
Gordon Raisbeck, was optimistic about the future of photovoltaics, speculating in 1955 that the new
devices would first find use where power is needed “in inaccessible places where no lines go” and “in
doing jobs the need for which we have not yet felt [12].”
Although commercial applications were difficult to find, the Air Force envisioned solar power
as an ideal technology for a new top-secret project—an earth-orbiting satellite. The Navy initially
rejected photovoltaics as an untested, unreliable technology, but finally allowed Vanguard, the first
U.S. satellite, to be launched with dual power systems of photovoltaics and chemical batteries.
The batteries died in nineteen days, but solar power kept Vanguard communicating with Earth
for years [13]. By the 1960’s photovoltaics had become the accepted power source for satellite
applications, opening a huge market for solar cell manufacturers.
Although the primary concerns for space photovoltaics were mass, efficiency, and durability, cost
was the limiting factor for terrestrial applications despite a drop in price from almost $300 per watt
in 1956 to $100 per watt by 1970. In the early 1970s, Dr. Elliot Berman, an industrial chemist
at Exxon Corporation, developed measures to reduce the cost of solar cells to $20 per watt by
using wafers rejected by the semiconductor industry, as well as cheaper packaging materials. The
fledgling terrestrial solar industry’s first customers were the oil and gas companies, whose offshore
rigs required warning lights and horns to prevent ships from running into them, and whose remote
fields required small amounts of electricity to reduce corrosion in well heads and pipes.
Over the next twenty years, the number of applications for terrestrial solar power grew prodigiously. The Coast Guard realized that it cost more to maintain the batteries which powered its
buoys than the buoys themselves, and replaced power systems in all of its buoys and lighthouses
with solar power. Telecom Australia, faced with a mandate to provide long-distance service and
television to every Australian citizen no matter how remote his location, developed a vast system of
solar-powered repeaters that became the model for remote telecommunications applications. Photovoltaic systems were also increasingly used in rural villages to pump water and provide basic power
needs, as well as on the rooftops and facades of urban buildings.

1.3

Photovoltaics present—current technology

1.3.1

Device operation

When light is incident upon a semiconductor material, photons with energy above the band gap
of the material are absorbed, and their energy can excite electrons from the valence band to the
conduction band of the semiconductor, creating electron-hole pairs. These carriers would normally
diffuse throughout the bulk semiconductor until they recombine with one another, but the presence
of a charge-separation structure such as a p-n junction, which can be created by doping the material,
allows a current to be collected.
The magnitude of the current collected from the solar cell is limited by the rate of carrier
recombination, which depends on the population of minority carriers in the device. These minority
carriers diffuse to a carrier-depleted region created by the p-n junction, whose internal electric field
accelerates them to the opposite side of the junction, where they become majority carriers. As
electron mobility in semiconductors is generally larger than hole mobility, photovoltaics are usually
designed such that most of the carrier generation occurs in a p-type layer, where electrons are the
minority carriers.

1.3.2

Materials for photovoltaics

Since only photons with energies above the band gap of a semiconductor are absorbed, the band gap
of the material used for a photovoltaic device must be engineered in order to produce the most power
for a given illumination, given that the solar spectrum is close to that of a blackbody at 6000 K,
as seen in Figure 1.1 (a). Semiconductors with larger band gaps produce higher photovoltages,
but absorb and convert fewer of the incident photons, resulting in lower currents; semiconductors
with smaller band gaps absorb most of the solar radiation, but convert most of the energy to heat.
In general, the solar cells with the best efficiencies use materials with band gaps near the peak of
the solar spectrum, between 1 and 2 eV [1]. The band gaps of many common semiconductors are
superimposed on the solar spectrum in Figure 1.1 (b).
Both direct band gap materials, such as the compound semiconductors GaAs, InP, CdTe, and CIS
(copper indium diselenide), and indirect band gap materials, like silicon, are used in the fabrication
of solar cells. While cells made with direct band gap materials may have higher efficiencies, silicon is
more abundant than the elements used to make compound semiconductors. The silicon photovoltaics
industry is also able to take advantage of the rejected raw materials and well-established infrastucture
for device processing provided by the microelectronics industry.
Both amorphous and crystalline (polycrystalline and monocrystalline) silicon are used in the
manufacture of photovoltaic devices. However, amorphous silicon suffers from the Staebler-Wronski
effect [14], in which dangling bonds are created under illumination, causing the efficiency to degrade

(a)

(b)

Figure 1.1: (a) Energy spectrum of solar radiation. The large absorption peaks are due mainly
to water and CO2 in the atmosphere. (b) Ideal cell efficiency as a function of band gap energy,
assuming no losses. The band gaps of several semiconductors used in photovoltaics are labeled. [1]
and capping the maximum efficiency at approximately 12%. We turn then to crystalline silicon
technology, which is capable of providing efficiencies greater than 20% [15].

1.3.3

Crystalline silicon technologies

The world record monocrystalline silicon solar cell is the PERL cell fabricated at the University
of New South Wales [16], which combines a passivated emitter, back surface field and front-side
texturing to achieve an efficiency of 24.5%. Commercially available cells, however, cannot reach the
efficiencies of laboratory cells, mostly due to the use of lesser quality substrates and limits imposed by
the contact screen-printing process. The best commercial monocrystalline cell is the A-300 module
manufactured by SunPower, which has contacts only on the back side, at 20.4% [17]. The Saturn cell
manufactured by BP Solar has displayed 18.3% efficiencies and uses a laser-grooved buried contact
on the front side [18].
Large-grained polycrystalline silicon material may be fabricated more cheaply than monocrystalline silicon by high-throughput processes such as casting or directional solidification to produce
multicrystalline ingots [15]. Although the majority and minority carrier properties of large-grained

polycrystalline silicon are close to those of monocrystalline silicon, it has been shown that the
presence of grain boundaries decreases the efficiencies of cells fabricated using this technology [19].
Commercial thick-film polycrystalline modules are available from Bayer, Sharp, and BP Solar; Kyocera’s KC module is the cheapest multicrystalline module at $3.16/Wp with 14% efficiency and the
Kyocera dBlue module is the most efficient at 15%.
Since approximately half the cost of a finished module comes from the material itself [20], thin-film
(<100 µm) crystalline solar cell technology has the potential to substantially reduce cost because a
smaller quantity of raw materials is used. Methods such as liquid-phase epitaxy (LPE) and chemical
vapor deposition (CVD) have produced high efficiency solar cells through deposition of thin epitaxial
films on crystalline silicon substrates. Werner et al. [21] report a 14.7% efficient cell with a 16.8 µm
active layer grown by LPE and an efficiency of 17.3% with a 20 µm active layer grown by CVD [22].
However, these techniques are not suited for low-cost production since costly crystalline silicon
wafers are still required as substrates and deposition rates are generally low (<5 Å/s). Evergreen
Solar has achieved 15% efficient cells by using a string ribbon growth process, by which an edgesupported 100 µm thick silicon ribbon is continuously pulled from a melt, rather than crystalline
silicon substrates [23].

1.4

Photovoltaics future—thin-film polycrystalline silicon?

The solar cell industry continues to grow, with worldwide production of solar modules increasing at
an average of 18% per year [24] while consumer module prices have decreased to less than $6 per
watt [25]. Power generation by photovoltaics, however, is still three to five times as expensive as
existing power generation methods. Based on electricity costs of 6c/kWh, in order for a photovoltaic
installation to be an attractive investment with a 10% after-tax return, a price of $1.50 per watt
must be realized [26].
One of the most promising technologies for reduced-cost photovoltaic modules involves the growth
of thin-film polycrystalline silicon on foreign substrates. Although the efficiencies of thin-film polycrystalline solar cells are lower than those of crystalline silicon cells, production costs are significantly
lower. In 1997 Astropower Corporation produced the first commercially available polycrystalline
silicon thin-film modules using a high-temperature process on a foreign substrate; although few
process details are known, laboratory cells with an active layer 50 µm thick displayed efficiencies of
16.6% [27].
Thin-film polycrystalline cells also eliminate some of the quality constraints placed on monocrystalline material which may require costly processing steps, since the minority carrier diffusion length
in the polycrystalline film need only be greater than its thickness. Thus even microcrystalline silicon
produces cells of moderate efficiency provided the active layer is 1–10 µm thick. Processes which en-

able deposition on low-cost substrates such as glass are particularly desirable, although the processing
temperature of the cell must then be kept below the glass transition temperature of the substrate.
Yamamoto et al. of Kaneka Corporation [28] have reported a 10.1% efficient microcrystalline cell on
glass with only a 2 µm thick active layer with a textured back reflector. Several low-temperature
deposition methods for polycrystalline silicon have been studied, including very-high frequency glow
discharge (VHF-GD) [29], plasma-enhanced chemical vapor deposition (PECVD) [28] and hot-wire
chemical vapor deposition (HWCVD), which is the focus of this study.

Chapter 2

Hot-Wire Chemical Vapor
Deposition
Hot-wire chemical vapor deposition (HWCVD) of silicon films involves the decomposition of gas
precursors on a heated refractory metal filament producing radical species which react in the gas
phase and deposit onto a heated substrate, as shown in Figure 2.1. The microstructure of the
resulting films is determined by several reactor parameters, such as the filament temperature, growth
pressure, gas flow rates, and substrate temperature.

2.1

Advantages for thin-film photovoltaics

Several aspects of the HWCVD process are especially suited to low-cost photovoltaic applications.
High deposition rates for amorphous [30] and polycrystalline [31] silicon have been reported which
can be up to one hundred times faster than PECVD. Deposition over a large area is possible with the
use of multiple-wire arrays – Ledermann et al. of the University of Kaiserslautern have demonstrated
uniform growth over a 20 × 20 cm area [32], and the ANELVA corporation has developed systems
designed for 1 square meter deposition [33]. Doped layers have been fabricated with the addition of
diborane or phosphine to the process [34].
Microcrystalline films grown by HWCVD display a columnar grain structure with <110> texture,
which may be advantageous for photovoltaics since carrier transport occurs along the columns rather
than across grain boundaries. Like PECVD, the HWCVD process produces great quantities of
atomic hydrogen, which provides in situ passivation of grain boundaries and defects [35]. However,
damaging ions that are produced by PECVD are not present in HWCVD. HWCVD-grown films also
display a controlled surface roughness, which may enhance light trapping in a photovoltaic device.

Figure 2.1: Schematic of the HWCVD process.

2.2

Development of HWCVD

In 1979, Wiesmann et al. [36] introduced HWCVD as a method which could produce hydrogenated
amorphous silicon (a-Si:H) films at high deposition rates, but the resulting films had inferior electronic properties compared to films grown by plasma enhanced chemical vapor deposition (PECVD).
Due to these poor results, the technique was virtually ignored until 1985, when Matsumura et al. [37]
demonstrated hydrofluorinated amorphous silicon films of high electronic quality using silicon difluoride and hydrogen precursors; in 1986, Matsumura produced high-quality a-Si:H under similar
deposition conditions [38]. They called the process “catalytic CVD” in the belief that the reaction
of hydrogen with the heated tungsten filament was catalytic in nature. Doyle et al. [39] also grew
high-quality a-Si:H under similar conditions in 1988, naming their process “evaporative surface decomposition” because the filament efficiently decomposed a low-pressure source gas, producing a
large flux of deposition radicals. Due to doubts regarding the catalytic reaction of hydrogen with
the filament, the process was renamed “hot-wire assisted CVD” in 1991 by Mahan et al.[40], whose
thorough comparisons of a-Si:H grown by HWCVD with that grown by PECVD led to tremendous
interest in the technique over the next ten years, as shown in Figure 2.2.

Figure 2.2: Number of papers on HWCVD published since its introduction in 1979. Matsumura
resurrected the technique in 1986. The First International Conference on Cat-CVD (Hot-Wire CVD)
was held in 2000, with the Second International Conference following in 2002.

2.3

Recent work in HWCVD

The a-Si:H films grown by Mahan et al. [40] were the first device-quality films to be grown by
HWCVD. These films had low hydrogen content (<1 atomic percent), which is important as it
is believed that hydrogen motion aids the formation of light-induced metastable defects via the
Staebler-Wronski effect [14, 41]. This problem in a-Si:H led to interest in the growth of microcrystalline and polycrystalline films by HWCVD – Matsumura was the first to obtain polycrystalline
films in 1991 [42], and in 1995 Heintze et al. [43] identified an amorphous-to-microcrystalline transition for HWCVD growth that occurs at a critical H2 :SiH4 ratio. Several studies of the effects
of various reactor parameters on the microstructural and electronic properties of microcrystalline
silicon have been performed [43, 44, 45]. Recently, Thiesen et al. [46] demonstrated epitaxial growth
on Si(100) by HWCVD at growth rates of up to 10 Å/s.

2.4

Thin-film HWCVD-deposited solar cells

The low hydrogen content of device-quality hot wire-deposited amorphous silicon films makes them
useful for inclusion in photovoltaics. In 1998, Bauer et al. at the University of Kaiserslautern recorded
an initial efficiency of 10.4% using a p-i-n structure on a glass substrate with the i-layer deposited by
HWCVD at low-temperature, although these cells degraded by approximately 30% when exposed
to light [47] . In 2000, Kaiserslautern reported 8.0% efficiency using hot-wire deposited p- and nlayers on ITO-coated glass [48]. Nelson et al. at NREL have reported initial efficiencies of 5.7% with
i-layers deposited at growth rates of 130 Å/s [30].
Microcrystalline silicon deposited by HWCVD has also shown promise as a material for solar cells.
Meier et al. [49] at the University of Neuchâtel have obtained 12% efficiency from a “micromorph”
cell using tandem µc-Si:H-a-Si:H cells on ITO-coated glass substrates; the total device thickness is
only 1.1 µm. Niikura et al. at École Polytechnique report a 4.6% efficient cell with an n-i-p structure
and a 2 µm thick i-layer grown at 300◦ C [50]. Rath et al. have fabricated an all-HWCVD n-i-p cell
with 3% efficiency [51].

2.5

Outline of the thesis

Empirically, it has been noted that solar cells made from material with the largest grain size have
the greatest open circuit voltages, for grain sizes between 1 µm and 1 mm [52]. In this study, we
investigate the fabrication of large-grained polycrystalline silicon by HWCVD and its suitability for
thin-film photovoltaic applications. We have devised two strategies for the fast, low-temperature
growth of thin polycrystalline silicon films on glass substrates. The first is the direct growth of
polycrystalline silicon on SiO2 by HWCVD. Here, we will show that the grain size can be controlled
by the addition of hydrogen to the process. Our observations of the nucleation kinetics of Si on SiO2
can be explained by a rate-equation pair-binding model (Chapter 3). The second strategy uses largegrained (∼100 µm) polycrystalline silicon layers fabricated by selective nucleation and solid-phase
epitaxy (SNSPE) on SiO2 substrates as templates for epitaxial growth by HWCVD. We will discuss
the microstructural properties of HWCVD-grown epitaxial films on Si(100) and SNSPE templates
(Chapter 4), as well as the minority carrier lifetimes and mobilities of these films (Chapter 5).

Chapter 3

Nucleation on SiO2
Abstract
We use atomic force microscopy (AFM) to characterize fully continuous polycrystalline silicon films
grown by HWCVD on SiO2 , as well as the nucleation density of silicon islands formed in the early
stages of HWCVD growth, as a function of temperature and H2 dilution (H2 :SiH4 ). We observe
an increase in grain size of continuous films with H2 dilution, from 40 nm using 100 mTorr of 1%
SiH4 in He to 85 nm with the addition of 20 mTorr H2 . This increase in grain size is attributed
to atomic hydrogen etching of Si monomers during the early stages of nucleation, which decreases
the nucleation density. The nucleation density increases sublinearly with time at low coverage,
implying a fast nucleation rate until a critical density is reached, after which grain growth begins.
The nucleation density decreases with increasing H2 dilution, which is an effect of the etching
mechanism, and with increasing temperature, due to enhanced silicon monomer diffusivity on SiO2 .
We apply a rate-equation pair binding model of nucleation kinetics [53] to the nucleation of
silicon islands grown by hot wire chemical vapor deposition on SiO2 substrates. From temperaturedependent nucleation density measurements, we estimate the activation energy for surface diffusion
of Si monomers on SiO2 during HWCVD growth to be 0.47±0.09 eV. Simulations of the temperaturedependent supercritical cluster density lead to an estimated activation energy of 0.42 eV±0.01 eV
and an estimated surface diffusion coefficient prefactor of 0.1±0.03 cm2 /s. H2 dilution-dependent
simulations of the supercritical cluster density show an approximately linear relationship between
the H2 dilution and the etch rate of clusters at H2 dilutions between 20:1 and 60:1. The model can
also be used to demonstrate possible strategies for the rapid growth of large-grained polycrystalline
films by HWCVD.

3.1

Introduction

A key issue for HWCVD films for large-grained thin-film photovoltaics is to identify growth conditions that enable the largest possible grain size at a given growth temperature with low intragranular defect density. Hydrogen is known to play a critical role in the development of a crystalline
microstructure in polycrystalline [42, 54, 55] films grown by HWCVD at low temperatures. Goodquality hydrogenated polycrystalline films are produced by the dilution of SiH4 in H2 —the hot wire
decomposes hydrogen molecules into hydrogen atoms which can etch silicon from strained or thermodynamically unfavorable bonding sites [43, 56], which leads to an amorphous to microcrystalline
transition. HWCVD proves more successful in the production of polycrystalline films of high crystalline fraction because the hot wire is a much more effective source for this atomic hydrogen than a
glow discharge [57], providing the proper balance of etching and hydrogenation of the silicon surface
during growth as well as creating radicals for deposition, which enhances the growth rate.
High-quality poly-Si:H films have recently been produced [55] which possess a high crystalline
volume fraction and a low density of defect states. Polycrystalline films grown by HWCVD without
hydrogen dilution have been shown to display a thin (<50 nm) amorphous incubation layer, from
which crystalline grains nucleate and grow to form a <220>-oriented columnar microstructure [58,
59, 60]. With the addition of H2 to the gas-phase precursors, this amorphous phase can be completely
eliminated, producing larger grains with reconstructed grain boundaries which need a hydrogen
concentration of less than 0.5 atomic percent to completely passivate them. This is shown to greatly
improve the electrical transport properties of these films [51], although the growth rate is decreased.
In our study, the role of atomic hydrogen produced by the wire in the etching of Si and its effect on
the resulting film microstructure are investigated through experiments and quantitative modelling
of the nucleation kinetics of Si on SiO2 at low substrate coverage.

3.2

Experiment

All film growth experiments were performed at base pressures of no higher than 1x10−6 Torr. Operating pressures were 100 mTorr of a mixture of 1% SiH4 in He, to which 20-140 mTorr of H2 was
added. A single straight tungsten wire of 12 cm length and 0.25 mm diameter was resistively heated
to 2000◦ C and positioned 2.5 cm from the substrate. The wire radiatively heated substrates consisting of 100 nm SiO2 on Si to 300◦ C; higher substrate temperatures were achieved by heating with
a resistive substrate heater in combination with the wire. H2 dilutions are referenced to 1 mTorr of
SiH4 in 99 mTorr He; all gases used are ultrahigh purity. A translatable shutter between the wire
and substrate enabled several growth experiments to be performed at low silicon coverage on each
substrate under identical gas ambient and wire temperature conditions, and also provided a definite

Figure 3.1: Schematic of hot-wire CVD experiments.
starting and ending point for film growth. A schematic of the experimental setup is displayed in
Figure 3.1.
In separate experiments, the substrate was replaced by a quartz deposition monitor (Inficon
XTC/2), which was used to measure the growth and etch rates of silicon as a function of H2 dilution
from 0-150:1, and by the orifice of a differentially pumped mass spectrometer (Hiden Analytical
Ltd., HAL RC201), with which the gas-phase radical species produced by the wire were measured.
Evidence for atomic hydrogen etching of silicon was demonstrated by H2 -dilution-dependent
measurements of the net Si growth rate, measured by the quartz crystal deposition monitor at the
substrate position, as well as by a separate experiment which measured the flux of SiH4 using a
differentially-pumped quadrupole mass spectrometer with orifice at the substrate position [61]. The
results of these experiments can be seen in Figure 3.2. A decrease in growth rate and corresponding
increase in SiH4 flux with increasing H2 dilution were attributed to atomic hydrogen etching of Si
species from the substrate and chamber walls and recombination of these species in the gas phase
to form SiH4 . A transition from net growth to net etching of silicon occurs with the addition
of approximately 80 mTorr of H2 . Since the silicon grown on the quartz deposition monitor is
amorphous, and crystalline silicon has been shown to etch more slowly than amorphous silicon under
atomic hydrogen exposure [56], the transition between net growth and net etching for crystalline
films likely occurs at a higher H2 dilution.
In subsequent experiments, the nucleation density at low Si coverage on a 100 nm SiO2 layer
was determined using contact-mode atomic force microscopy (AFM), as illustrated in Figure 3.3(a).
This image was taken after a growth time of 90 seconds at 20:1 H2 dilution. For each sample, 5 scans
of 25 µm2 were performed; the observable nuclei were then counted for each scan and the resulting
numbers of nuclei were averaged. As seen in Figure 3.4, which displays the nucleation data as a

0.8

0.008

SiH 4 mol fraction
Net growth rate

0.6

0.007
0.006
0.005

0.2
0.004
0.0
0.003
-0.2
0.002

transition from net growth
to net etching

-0.4

SiH 4 mol fraction

Net growth rate (Å/s)

0.4

0.001

-0.6

100

120

140

0.000
160

H 2 pressure (mTorr)

Figure 3.2: Net deposition rate and SiH4 mole fraction as a function of H2 partial pressure in
100 mTorr of dilute SiH4 1% in He.
function of H2 dilution at 300◦ C, the nucleation density increases sublinearly with time, implying
a nucleation rate which is initially high until a critical density of nuclei is reached, at which time
the nucleation rate is sharply reduced and grain growth begins. Exposing the SiO2 substrates to
60 mTorr H2 for 10 minutes before growth had no effect on the nucleation density, demonstrating
that exposure to H2 does not appreciably etch or roughen the surface of the SiO2 . The nucleation
density was highest for no added H2 and decreased with H2 dilution. This result is consistent with
the AFM micrographs in Figure 3.3(b) and (c), which indicate an increase in grain size in thick,
continuous films (∼200 nm) from 40 nm with no H2 dilution to 85 nm at a H2 dilution of 20:1.
The nucleation density also decreased with increasing temperature due to enhanced diffusivity of Si
monomers on SiO2 . From the temperature-dependent nucleation density measurements performed
at substrate temperatures of 300-450◦ C presented in Figure 3.5, we estimate the activation energy
for surface diffusion of Si on SiO2 to be 0.47±0.09 eV.

Figure 3.3: (a)AFM of the HWCVD nucleation phase. This image was taken after a growth time of
90 seconds at 20:1 H2 dilution. Bright features are ≥35 nm in height. (b) Post-coalescence 1 µm2
image of a continuous poly-Si film grown at zero H2 dilution; grain size is 40 nm. (c) Post-coalescence
1 µm2 image of a continuous poly-Si film grown at 20:1 H2 dilution; grain size is 85 nm.

1.2x10

8.0x10

6.0x10

4.0x10

2.0x10

Nucleation density (cm

-2

1.0x10

0 H2
0 H 2 exposed
20:1 H 2
40:1 H 2
60:1 H 2
80:1 H 2

0.0

200

400

600

800

1000

Time (s)

Figure 3.4: Nucleation data as a function of H2 dilution at 300◦ C. The lines are a guide to the eye.

1.2x10

1.0x10

8.0x10

6.0x10

4.0x10

2.0x10

Nucleation density (cm

-2

300 C
350 C
400 C
450 C

0.0

100

120

140

Time (s)

Figure 3.5: Temperature-dependent nucleation measurements. The lines are a guide to the eye. The
initial slope of the data were used to estimate the activation energy for surface diffusion of Si on
SiO2 .

3.3

Quantitative modelling

We quantitatively model the observed nucleation kinetics of Si on SiO2 through a rate-equation pair
binding framework developed by Venables [53], which assumes that only monomers n1 (which could
be Si adatoms or adsorbed SiH3 molecules) are mobile on the surface. The equations governing the
density nj of clusters of size j are
n1
d(nx wx )
dn1
=R−
dt
τa
dt

(3.1)

dnj
= 0 (2 ≤ j ≤ i)
dt

(3.2)

dZ
dnx
= σi Dn1 ni − 2nx
dt
dt

(3.3)

Equation 3.1 describes the evolution of the monomer population n1 due to arrival of atoms from
the gas phase at rate R, evaporation with time constant τa , and incorporation into existing clusters,
where nx wx is the total number of atoms in existing clusters. Equation 3.2 gives a thermodynamic

17
equilibrium between subcritical clusters smaller than the critical size i, and Equation 4.6 gives
the supercritical cluster density nx in terms of a nucleation rate σDn1 ni and a coalescence rate
proportional to Z, the rate of change of the substrate coverage by stable clusters. Equations 3.1
and 3.3 are coupled by the interaction between nucleation and growth, whereby single adatoms are
incorporated into stable clusters by nucleation, diffusion capture, and direct impingement, so that
n1
d(nx wx )
n1
+ RZ
dt
τn
τc

(3.4)

where τc −1 = σx Dnx . The nucleation term τn is unimportant numerically and can be ignored; the
capture numbers σ [62, 63] and the diffusion coefficient D = D0 exp[Ea /kT ] are given by the solution
of the two-dimensional diffusion equation on the substrate. For complete condensation conditions,
the theory can be used to predict the stable cluster density, which depends on the activation energy
for surface diffusion (Ea ) and lateral binding energy (Eb ) [63].
For a critical cluster size i=1, which predicts the lowest monomer density on the surface, a lateral
binding energy for silicon clusters Eb =1.55 eV [64] and for a rate R=5x1010 cm−2 s−1 (determined
by calculating the total volume of Si deposited on the substrate from AFM images), we estimate
the diffusion coefficent prefactor D0 and the activation energy Ea for Si diffusion on SiO2 by using
the model to fit the temperature-dependent supercritical cluster density measurements, as seen in
Figure 3.6, under complete condensation conditions, i.e., assuming that no etching occurs under
pure SiH4 conditions. It should be noted that a critical cluster size i=1 implies that there is no
barrier to nucleation. The data are best approximated with values of D0 =0.1 cm2 /s and Ea =0.42
eV. Increasing the activation energy causes the linear regime of the simulated supercritical cluster
density curves to persist for longer times, while increasing D0 causes the family of curves to display
an increased supercritical cluster density. The simulated curves fit the experimental data within a
factor of two; the simulation parameters were chosen so as to generally overestimate rather than
underestimate the experimental cluster densities, as it is reasonable that supercritical clusters exist
on the substrate which cannot be resolved with the AFM. The simulated value of Ea is within the
error of the least-squares fit used to determine the activation energy experimentally.
To model the effects of H2 dilution at substrate temperatures of 300◦ C and 400◦ C, the adatom
stay time τa was modified to account for the etching of monomers from the substrate by atomic
hydrogen. The results are shown in Figure 3.7. Here, the data at H2 dilutions from 20:1-60:1 are not
overestimated, but are fit as closely as possible in order to determine the relative etch rates for the
different H2 dilutions. The difference in the values of τa at identical dilution for the two different
temperatures suggests a temperature-dependent reactive etching mechanism for Si monomers by
atomic hydrogen. The rate at which adatoms are etched from the substrate by atomic hydrogen
should be proportional to the etch yield Y of Si by atomic hydrogen, the flux ΦH of atomic H at

1.6x10

Supercritical cluster density (cm -2)

1.4x10

1.2x10

1.0x10

8.0x10

6.0x10

4.0x10

2.0x10

300 C
350 C
400 C
450 C

0.0

100

120

Time (sec)

Figure 3.6: Comparison of simulated (lines) and experimental (dots) temperature-dependent cluster
density measurements.
the surface, and the fraction fn1 of the substrate covered by monomers, such that
= Y ΦH fn1
τa

(3.5)

Simulation predicts a maximum monomer concentration on the order of 106 cm−2 and a value for
fn1 of order 10−9 . ΦH is on order 1016 cm2 s−1 . The etch rates (on the order of 10−6 ) predicted by
the simulation in turn predict a reasonable etch yield of Si by atomic hydrogen of Y =0.1. These etch
rates show an approximate linear relationship with H2 dilution, shown in Figure 3.8. This suggests
that atomic hydrogen etching of monomers, rather than competitive etching of stable, supercritical
amorphous and crystalline nuclei, may be the dominant process governing the nucleation kinetics at
low coverage. The etch yield also appears to be temperature-dependent, which, in addition to the
difference between the critical cluster size and the observable cluster size, may add to the discrepancy
between the predicted and experimental temperature-dependent data.

-2

Supercritical cluster density (cm

8.0x10

6.0x10

4.0x10

2.0x10

8.0x10

6.0x10

4.0x10

2.0x10

0 H2
20:1 H 2
40:1 H 2
60:1 H 2

1.0x10

0 H2
20:1 H 2
40:1 H 2
60:1 H 2

-2

1.2x10

Supercritical cluster density (cm

1.4x10

0.0

200

400

600

800

1000

200

400

600

800

1000

1200

Time (sec)

Adatom stay time (s)

Figure 3.7: Comparison of simulated and experimental H2 dilution-dependent cluster density measurements at (a) 300◦ C and (b) 400◦ C.

2.5x10

-5

2.0x10

-5

1.5x10

-5

1.0x10

-5

5.0x10

-6

300 C
400 C

0.0
20

H 2 dilution

Figure 3.8: Adatom stay time as a function of H2 dilution.

3.4

Microstructural control

We also investigate strategies for the fast growth of large-grained polycrystalline films by HWCVD.
One such strategy is to first grow a low-density layer at high H2 dilution, which will serve as a seed
layer for the fast growth of large grains at low H2 dilution [65]. To test this strategy experimentally,
a low-density seed layer was grown at 300◦ C at an H2 dilution of 60:1. After one thousand seconds,
the H2 dilution was reduced to zero, and growth was allowed to proceed for 300 seconds. Although
this strategy could have been further optimized, the results, displayed in Figure 3.9, are encouraging
– although the nucleation density does increase compared to continued growth at 60:1 H2 dilution,

Nucleation density (cm

-2

it is indeed suppressed with respect to growth at 0 H2 dilution.

1.4x10

1.2x10

1.0x10

8.0x10

6.0x10

4.0x10

2.0x10

0 H2
60:1 H 2
Two-stage growth

0.0

200

400

600

800

1000

1200

Time (sec)

Figure 3.9: Two-stage growth experiment, as compared to undiluted growth and growth at 60:1 H2 .
The lines which fit the data at 0 H2 and 60:1 H2 are guides to the eye.
The pair-binding model enables us to model this behavior, as well as consider more interesting
strategies. As an example, we consider a case similar to an experiment performed by Rath et al.[66],
where a seed layer is again grown at 60:1 H2 dilution, after which the H2 dilution is gradually
ramped down to zero over the next 700 seconds. As seen in Figure 3.10, this strategy proves more
effective in suppressing the nucleation density than the two-stage growth strategy. Table 3.1 shows
the time necessary for the grains of polycrystalline films to coalesce as well as the grain density of

21
Table 3.1: Coalescence times and grain densities of continuous films under various H2 dilution
conditions, as predicted by the pair-binding model.
H2 dilution

Coalescence time (s)

Continuous film grain density (cm−2 )

60:1
Two-stage
Ramp

12000
5000
7500

2.3 x 109
3.0 x 109
2.6 x 109

the resulting continuous films as predicted by the pair-binding model. The model predicts that films
grown under ramped dilution will not only coalesce faster than those grown at 60:1 dilution, but

Supercritical cluster density (cm -2)

possess a lower grain density than those produced by the two-stage growth condition.

2.5x10

2.0x10

1.5x10

1.0x10

5.0x10

Two-stage growth
60:1 H 2 (300 s), 0 H 2

Ramp dilution
60:1 H 2 (300 s)
to 0 H 2 at 1000s

60:1 H 2

0.0

500

1000

1500

Time (sec)

Figure 3.10: Pair-binding model simulations of growth at 60:1 H2 dilution, two-stage growth, and
ramped dilution.

3.5

Conclusions

An increase in grain size of continuous polycrystalline silicon films with H2 dilution can be attributed to atomic hydrogen etching of silicon monomers, decreasing the nucleation density. Experiments show that the nucleation density increases sublinearly with time at low coverage, implying

22
a fast nucleation rate until a critical density is reached, after which grain growth begins. Through
temperature-dependent nucleation-density measurements, the activation energy for diffusion of Si
monomers on SiO2 during HWCVD growth is estimated to be 0.47±0.09 eV. To our knowledge, this
is the first estimate for this activation energy given in the literature.
The experimental nucleation density measurements can be understood within the framework of
a rate-equation pair-binding simulation. Modelling of the temperature-dependent cluster density
measurements give D0 =0.1±0.03 cm2 /s and Ea =0.42±0.01 eV, which is within the error in the
experimentally determined value. Monomer etching by atomic hydrogen is simulated by changing
the adatom stay time τa , and the simulated etch rates vary approximately linearly with H2 dilution.
The model can also be used to explore possible strategies for the rapid growth of large-grained
polycrystalline films by HWCVD.

Chapter 4

Epitaxial Growth by HWCVD
Abstract
We investigate the low-temperature (300–475◦ C) epitaxial growth of thin silicon films by hot-wire
chemical vapor deposition on Si(100) substrates and on large-grained polycrystalline template layers
formed by selective nucleation and solid phase epitaxy (SNSPE). Using reflection high energy electron
diffraction (RHEED) and transmission electron microscopy (TEM), we have derived a phase diagram
for Si on Si(100) consisting of epitaxial, twinned epitaxial, mixed epitaxial/polycrystalline, and
polycrystalline phases of growth on Si(100) in the 50 nm–2 µm thickness regime. Evidence is also
presented for epitaxial growth on SNSPE templates, which use nickel nanoparticles as nucleation
sites for the solid-phase crystallization of phosphorus-doped amorphous silicon on SiO2 .

4.1

Introduction

HWCVD has been shown to be a promising method for fast, low-temperature (<600◦ C) epitaxy [46,
67, 68]. Previously, we showed that direct deposition by HWCVD on SiO2 produced small grains
(40–80 nm), even with the addition of H2 to a dilute mixture of 1% SiH4 in He. Our second strategy
for the fabrication of large-grained polycrystalline silicon photovoltaics uses a polycrystalline silicon
layer with grain size on the order of 100 µm as a template for epitaxial growth by HWCVD. These
layers are formed using nickel nanoparticles as nucleation sites for the solid-phase crystallization
of phosphorus-doped amorphous silicon on SiO2 and have been successfully used as seed layers
for epitaxial growth by molecular beam epitaxy (MBE) at temperatures below 600◦ C [3, 69]. In
this chapter, we will discuss the microstructural properties of epitaxial films grown by HWCVD on
Si(100) substrates and polycrystalline templates.

4.2

Low-temperature epitaxy

There are several means of growing epitaxial silicon films at low temperature. In one class of
processes, which includes MBE and low-pressure chemical vapor deposition (LPCVD), increasing
the growth temperature generally leads to an increase in the maximum attainable epitaxial film
thickness [70]. A critical bulk concentration of atomic hydrogen leads to the premature breakdown
of epitaxy [71], although epitaxial silicon can be deposited by MBE on a surface covered with one
monolayer of hydrogen [72]. At low surface coverages, hydrogen atoms act as a diffusion barrier for
silicon atoms, thus dramatically increasing the Si island density, accelerating an increase in surface
roughness, and causing early epitaxial breakdown by a transition from crystalline to amorphous
growth [73].
Other processes, such as plasma-enhanced chemical vapor deposition (PECVD) and HWCVD,
involve high gas pressures and deposition sources that are also efficient sources of atomic hydrogen,
which can abstract surface hydrogen and etch silicon. In such processes, an increase in growth
temperature does not necessarily lead to an increase in epitaxial thickness. Since growth proceeds
by abstraction reactions, it is the concentration of hydrogen at the surface rather than the bulk
concentration that may affect the limiting thickness of epitaxial growth. A balance between the
flux of atomic hydrogen incident on the growth surface and the thermal desorption of hydrogen may
be required [74]. Upon the breakdown of epitaxy, films grown by these processes often undergo a
transition to polycrystalline growth rather than a transition to amorphous growth [75].

4.3

Epitaxy on Si (100)

4.3.1

Initial experiments

4.3.1.1

Growth conditions

Silicon films of 300 nm thickness were grown on Si(100) substrates by HWCVD at temperatures
between 300-450◦ C using 70 mTorr H2 at 20 sccm and 100 mTorr dilute SiH4 in He at 20 sccm.
A 0.5 mm diameter tungsten filament was heated to 1850◦ C and placed 5 cm from the substrate,
resulting in a growth rate of 0.15 Å/s. These initial conditions were chosen to produce amorphous
silicon films on SiO2 , similar to those investigated by Seitz et al. [67]. Substrates were cleaned with
UV-ozone for 10 minutes and dipped in hydrofluoric acid, then heated to 200◦ C in vacuum to desorb
hydrocarbons [76]. Ultra-high purity gas mixtures were used and the base pressure of the growth
chamber was below 10−6 Torr.

Figure 4.1: Cross-sectional TEM of HWCVD-grown Si on Si (100) at 300◦ C. The epitaxial films
display a periodic array of stacking faults.
4.3.1.2

Results

Cross-sectional TEM of films grown on Si(100) substrates at 300◦ C confirms the presence of epitaxial growth, as shown in Figure 4.1. The rough film-substrate interface is believed to have been
caused by etching of the surface during growth by atomic hydrogen produced by the wire [77]. The
roughened appearance of the silicon substrate in cross-section may be due to the presence of hydrogen platelet defects arising from the diffusion of hydrogen into the film during growth, although
the exact structure of the defects has yet to be determined. Epitaxy continues to a thickness of
approximately 240 nm, after which the film becomes highly twinned, as seen in Figure 4.2 (a). The
epitaxial films exhibit a periodic array of stacking faults which gives rise to the higher-order spots
seen in the diffraction patterns in Figure 4.2 (b) and (c).
TEM of films grown at 400◦ C, shown in Figure 4.3, reveals mixed phase growth with some areas
of epitaxial growth at the interface and a quick transition to polycrystalline growth as seen in the
diffraction pattern. More prominent hydrogen-induced defects are present in the substrate, perhaps
due to the enhanced diffusion of hydrogen into the substrate at higher temperatures.

Figure 4.2: (a) Cross-sectional TEM of HWCVD-grown Si on Si (100) at 300◦ C. The films become
highly twinned after a thickness of approximately 240 nm. Labels b, c, and d refer to areas from which
selected-area diffraction patterns were obtained. (b) Selected area diffraction from HWCVD film
and amorphous glue layer. (c) Selected area diffraction from HWCVD film and Si (100) substrate.
(d) Selected area diffraction from Si (100) substrate. Higher-order spots in (b) and (c) are due to
the periodic array of stacking faults in the epitaxial film and twinning in the uppermost regions of
the film.

H-induced
defects
film
substrate

30 nm

Figure 4.3: Cross-sectional TEM of HWCVD-grown Si on Si (100) at 400C◦ , which displays mixed
epitaxial/polycrystalline growth. Hydrogen-induced defects are present in the substrate.

4.3.2

Further experiments

4.3.2.1

Growth conditions

The epitaxial films discussed in section 4.3.2.2 were grown in a reconfigured reactor using a mixture
of 4% SiH4 in He at a pressure of 25 mTorr and a flow rate of 16 sccm, providing the same amount of
SiH4 in the reactor as in the previous experiments. Under these conditions, the maximum achievable
H2 :SiH4 ratio was 50:1, using 50 mTorr H2 at a flow rate of 52 sccm. The wire was positioned at a
distance of 2.5 cm from the substrate in order to increase the growth rate to 1 Å/s for diluted growth.
This required a decrease in wire temperature to 1800◦ C in order to minimize tungsten incorporation
into the films. The wire radiatively heated the substrate to 300◦ C and, with the addition of a separate
resistive heater, substrate temperatures up to 475◦ C could be achieved. Under these conditions,
undiluted growth at all temperatures produced polycrystalline films. Vacuum pressures were kept
below 5×10−7 Torr and inline gas purifiers (Nanochem MiniSentry) were added to the system to
further decrease carbon and oxygen contamination.
Before growth, surfaces were cleaned with UV ozone for 10 minutes, dipped in HF, and heated to
200◦ C in vacuum to desorb hydrocarbons as before. Since low doses of atomic hydrogen have been

28
shown to be an effective in-situ method for removing surface carbon and oxygen[78, 79, 80] residual
hydrocarbons [81, 82] and submonolayer oxides [83], for these experiments an additional atomic
hydrogen cleaning step was added. If the dose is kept below 300-400 Langmuir, no appreciable
surface roughening should occur [84]. Samples were cleaned for 5 minutes with atomic hydrogen at
an H2 flow rate of 2.2 sccm, corresponding to a chamber pressure of approximately 10−4 Torr. We
estimate the total dose of atomic hydrogen to which the substrate is exposed by considering the wire
as an effusion source of atomic hydrogen. The relation
Peq
Γ= p
(2π)mkT

(4.1)

where Peq is the chamber pressure, m is the mass of a hydrogen atom, k is Boltzmann’s constant
and T is the temperature of the wire, can be used to calculate the flux of hydrogen Γs at the wire
and subsequently at the substrate, assuming a geometry where the wire and substrate are concentric
cylinders[85]. Assuming that all hydrogen molecules dissociate on the wire, we calculate that the
maximum total dose of atomic hydrogen to which the sample is exposed during the cleaning is
360 L. AFM measurements on an unexposed Si(100) substrate and one exposed to a 360 L atomic
H dose showed that no observable roughening of the surface takes place during the atomic hydrogen
cleaning. Exposure to doses of atomic hydrogen below this threshold has also been shown not to
affect hydrogen surface coverage [75].
Films were grown at an H2 :SiH4 ratio of 50:1 at substrate temperatures from 300–475◦ C. Using
the translatable shutter described in Chapter 3, we were able to grow films of several different thicknesses under identical growth conditions. The microstructure of the resulting films was characterized
by TEM, RHEED and AFM.
4.3.2.2

Results

Transmission electron microscopy

Figure 4.4 shows TEM micrographs of a film grown at

300◦ C to a thickness of 350 nm. Figure 4.4 (a) gives evidence for epitaxial growth to a thickness
of approximately 50 nm, followed by the emergence of stacking faults and twin boundaries which
give rise to the extra spots in the diffraction pattern. The contrast at the film/substrate interface
is likely due to submonolayer contamination, possibly by tungsten. Figure 4.4 (b) shows that the
stacking faults and twinning extend from the initial 50 nm epitaxial layer through the full thickness
of the epitaxial film.
The 15 µm thick film in Figure 4.5 (a) displays twinned growth directly from the interface, probably due to inadequate surface preparation. A mixed phase of twinned epitaxial and polycrystalline
growth is observed (Figure 4.5 (b)), with regions of twinned crystalline growth extending as far as
300 nm into the film. The grain size of the polycrystalline film is on the order of 1 µm. The average

film

30 nm

substrate

85 nm

Figure 4.4: Cross-sectional TEM of 350 nm-thick film grown at 300◦ C. (a) 50 nm-thick epitaxial
layer before twinned growth begins. Inset: diffraction pattern from twinned region; (b) Twinning
continues throughout film growth.
growth rate for the polycrystalline film was 2.3 Å/s, which is more than twice as large as the growth
rate of 1 Å/s calculated for thin epitaxial films. The increased deposition rate for polycrystalline
films may be due to an increase in the number of possible growth sites as the film surface roughens.
Reflection high-energy electron diffraction

RHEED is a technique which provides informa-

tion about sample surface morphology. A 25 keV electron beam was incident upon the sample surface
at a grazing angle of 1.5◦ . The resulting elastic scattering features from the surface provide qualitative information about the surface morphology. We found that these features correlate well with the
microstructure observed by TEM, eliminating the need for tedious sample preparation and analysis.
Although the measurements described here were performed in a separate chamber, RHEED could
easily be incorporated into a HWCVD reactor to allow the in situ observation of surface morphology
at various stages of growth, although the high growth pressures used in HWCVD would make it
necessary to stop growth before each RHEED measurement.
Figure 4.6 shows the RHEED patterns of several films grown at 300◦ C. At 60 nm [Figure 4.6(a)],
double diffraction spots of lesser intensity than the main Si (100) spots first appear, indicating
twinned growth. These double diffraction spots correlate with the TEM images in Figure 4.4, in
which the onset of twinning is observed at a thickness of approximately 50 nm. The double diffraction

poly

substrate
twinned

film

substrate
10 nm

25 nm

1.5 µm

Figure 4.5: Cross-sectional TEM of 15 µm thick film grown at 300◦ C. (a) Stacking faults and
twinning begin at interface. (b) Mixed twinned epitaxial/polycrystalline growth; twinned regions
extend as far as 300 nm into film. (c) Grain size of polycrystalline film is on the order of 1 µm.

60 nm b

120 nm c

180 nm

240 nm

330 nm f

660 nm g

1050 nm h

2000 nm

Figure 4.6: RHEED patterns of films of increasing thickness grown at 300◦ C. The beam is along
the <110> direction. Two phases of growth are observed: twinned epitaxial growth [a-g] and
polycrystalline growth [h].
spots increase in intensity as the films grow thicker, indicating that twinned epitaxial growth persists
to a thickness of 1 µm, and new spots related to surface roughening appear [86]. At a thickness of 2
µm, a ring pattern consistent with a transition to polycrystalline growth is observed [Figure 4.6(h)].
Atomic force microscopy

AFM (Park Autoprobe) was used to characterize the surface rough-

ness of a series of films grown at 300◦ C from 60 nm to 1 µm in thickness. The 4x4 µm topography
and error mode images in Figure 4.7 show an increase in surface roughness from 4.1 nm for a 60 nm
thick film to 17.6 nm for a 1 µm thick film. Line scans determined that the lateral dimension of the
surface features increased from approximately 0.14 µm for the 60 nm thick film to approximately
1 µm for the 1 µm thick film. The size of the secondary surface features on the 1 µm thick film is
approximately 0.16 µm. Many of these surface features appear to be aligned with the (001) direction.
Substrate temperature effects We used TEM and RHEED to characterize the crystallinity of
films grown at 50:1 hydrogen dilution and temperatures between 300–475◦ C in the 50 nm–2 µm
thickness regime and observed four phases of growth. The epitaxial phase was observable only
by TEM at thicknesses below 50 nm (Figure 4.4); the twinned epitaxial, mixed and polycrystalline
phases were observable by TEM (Figure 4.5 and RHEED as illustrated in Figure 4.8. From this data,
we derived the phase diagram in Figure 4.9. At 300◦ C, the predominant phases are epitaxial and
twinned, with a transition to mixed phase or polycrystalline growth occuring somewhere between 1
and 2 µm of growth. As temperature increases, the epitaxial and twinned phases no longer persist

1 µm

t = 120 nm

t = 180 nm

t = 240 nm

t = 330 nm

t = 1050 nm

t = 60 nm

Figure 4.7: 4x4 µm AFM topography (top panels) and error mode (bottom panels) images of films
of increasing thickness grown at 300◦ C.

Figure 4.8: Phases of crystalline growth observable by RHEED. (a) 300◦ C, 60 nm thick twinned
epitaxial film. (b) 300◦ C, 330 nm thick twinned epitaxial film; increased surface roughness is responsible for the differences from (a). (c) 475◦ C, 60 nm thick film of mixed phase; both spots
(corresponding to twinned epitaxial growth) and rings (corresponding to polycrystalline growth) are
evident. (d) 475◦ C, 330 nm thick polycrystalline film.
and the transition to mixed phase or polycrystalline growth occurs at smaller film thicknesses.

4.3.3

Discussion

The results reported here for hydrogen-diluted epitaxial growth on Si(100) are broadly consistent
with work reported elsewhere. Theisen et al. observed epitaxial growth with stacking fault defects at
temperatures between 195 and 325◦ C [46], while Seitz and Schröder observed no stacking faults or
surface roughening in their epitaxial films grown between 280 and 360◦ C [67]. Both experiments were
done using approximately 10 mTorr of pure SiH4 and no additional hydrogen. Although Thiesen
et al. postulate that the reason that low-temperature epitaxy by HWCVD is possible because the
growth species is SiH3 , we believe that for our dilute silane conditions the dominant growth species
are silicon atoms [77].
Kitagawa et al. [75] report that, at 430◦ C, the critical thickness hepi for Si epitaxy by PECVD

Figure 4.9: Phase diagram of HWCVD films grown at 50:1 hydrogen dilution.
increases monotonically with hydrogen dilution at constant pressure, while at 120◦ C, there is an
optimal hydrogen dilution which produces the greatest value of hepi . Kondo et al. [74] propose a
model for epitaxial growth in atomic hydrogen-rich processes in which hepi depends on the homogeneous surface hydrogen coverage of the Si(100) surface. At high temperatures, Si(100) undergoes
a 2×1 reconstruction with monohydride coverage [2]. The thermal desorption rate of hydrogen is
high, and thus a high flux of atomic hydrogen is required to maintain this hydrogen coverage. At
low temperatures, the Si(100) surface displays a 1×1 dihydride reconstruction. Here, it is thought
that a flux of atomic hydrogen which is too high may lead to the abstraction of surface hydrogen
and the formation of a monohydride surface. Therefore, a balance between the thermal desorption
of hydrogen from the surface and the atomic hydrogen flux density is required for the persistence of
epitaxial growth.
We consider a model for the thermal desorption of hydrogen proposed by Flowers et al. [87]
in which the overall rate of change of the fractional coverage Θ of the Si(100) surface during
temperature-programmed desorption can be determined by considering the Si(100) surface as an

35
ensemble of 1×1 and 2×1 lattice sites which are occupied by indistinguishable hydrogen atoms. θ00 ,
θ10 , θ11 and θ2 represent the fractional coverages of unoccupied dimers, singly occupied dimers,
doubly occupied dimers, and dihydride species, respectively. It must be true that

θ00 + θ10 + θ11 + θ2 = 1

(4.2)

θ10 + θ11 + 2θ2 = Θ

(4.3)

and

If a quasi equilibrium state for the reactions

H-Si-Si-H + Si=Si *
) 2H-Si-Si

(4.4)

H-Si-Si-H *
) H-Si-Si · +H-Si-H

(4.5)

and

is assumed, the distribution of surface species can be calculated from their vibrational partition
functions. If the only significant differences in vibrational partition functions for the surface groups
are due to Si-H vibrations then the equilibrium between surface species can be described by

θ10
4Q210
exp −
θ00 θ11
Q11
kT
θ10 θ2

1 =

3 (1 + θ ) 2
θ11

exp
kT
(Q311 ) 2
Q10 Q2

(4.6)

(4.7)

where the Q’s represent the vibrational partition functions for surface species

νi
exp(− kT
νj .
j exp −( kT )

(4.8)

The Si-H vibrational frequencies can be obtained from published data. By solving Equations
4.2, 4.3, 4.6 and 4.7 for a particular hydrogen coverage and surface temperature, the equilibrium
distributions of all surface species on Si (100) can be calculated.
Considering adsorption, abstraction and thermal desorption of hydrogen from the surface, the
rate of change of the surface hydrogen coverage on Si(100) during HWCVD growth at a specific
temperature is given by
dΘ
dΘ
dΘ
dΘ
dt
dt adsorption
dt abstraction
dt desorption

(4.9)

36
Table 4.1: Parameters used in hydrogen surface coverage model.
Parameter
νa
Ea
νb
Eb
1
2
H-SiSi stretch
H-SiSi bend
H-Si-Si-H sym. stretch
H-Si-Si-H asym. stretch
H-Si-H deformation
H-Si-H sym. stretch
H-Si-H asym. stretch
H-Si-H scissors
Pads
Eads
Pabs
Eabs

Value
2×101 5 s−1
57.2 kcal/mol
3.2×101 3 s−1
43 kcal/mol
6.0 kcal/mol
19 kcal/mol
2093 cm−1
621 cm−1
2088 cm−1
2099 cm−1
637 cm−1
2091 cm−1
2104 cm−1
910 cm−1
0.6
0.1 kcal/mol
0.52
2.0 kcal/mol

Reference
[89]
[89]
[90]
[87]
[89]
[87]
[87]
[91]
[92]
[92]
[91]
[93]
[93]
[90]
[94]
[95]
[96]
[97]

where
dΘ
Eads
= ΦH Pads exp −
(2 − Θ),
dt adsorption
kT

(4.10)

dΘ
Eabs
= ΦH Pabs exp −
Θ,
dt abstraction
kT

(4.11)

dΘ
= νa × θ11 × exp(−Ea /kT ) + νb × θ22 × exp(−Eb /kT )
dt desorption

(4.12)

and

as before.
The reaction constants νa and νb and activation energies Ea and Eb , as well as parameters
for the adsorption probability Pads exp(−Eads /kT ) and abstraction probability Pabs exp(−Eabs /kT )
are also found in the literature. A comprehensive list of parameters used in the model are listed in
Table 4.3.3. The flux of hydrogen at the surface ΦH can be determined from equation 4.1 as before.
The cracking probabilities of SiH4 and H2 on the wire are taken as 0.7 and 0.14, respectively [88].
By setting equation 4.9 equal to zero, we can determine the equilibrium surface coverage of
Si(100) during HWCVD growth as a function of temperature under various growth conditions. At
low temperatures, thermal desorption is negligible and a balance is reached between adsorption and

37
abstraction of hydrogen. At high temperatures, thermal desorption becomes more significant. The
calculated equilibrium surface coverages for our initial and revised growth conditions are plotted in
Figure 4.10, with the experimental equilibrium surface coverage data of Gates and Kulkarni [2] for
temperature-programmed desorption given for comparison. Under HWCVD growth conditions the
equilibrium surface coverage is higher than that which would be reached if thermal desorption were
the only mechanism affecting the hydrogen coverage.

Figure 4.10: Calculated equilibrium surface hydrogen coverages for HWCVD growth conditions
(H2 :SiH4 =50:1, 25 mTorr 4% SiH4 in He, wire 2.5 cm from substrate), with experimental
temperature-programmed desorption data [2] for comparison. The shaded area represents the temperature regime in which HWCVD growth experiments were performed.
We hypothesize that the incorporation of contaminants, i.e., oxygen adsorption, contributes to
epitaxial breakdown. When the ratio of silicon to oxygen deposition is highest, the greatest hepi
may be achieved, although the exact correspondence between hepi and the silicon to oxygen ratio is
unknown. The oxygen flux ΦO2 at the substrate can also be determined using equation 4.1 using
the mass of molecular oxygen and the substrate temperature; the partial pressure of oxygen in the

38
chamber is approximately 1×10−7 Torr at a base pressure of 5×10−7 Torr. The oxidation rate at
the equilibrium surface coverage for a given temperature is
dΘ
= ΦO2 Pox θ00 + θ10
dt oxidation

(4.13)

where Pox = 0.01 and is roughly temperature-independent [98].
Starting with an initial surface coverage dependent only on the substrate temperature, we use
the model to compute the amount of oxygen deposited during the growth of the first monolayer of
silicon for a given growth temperature as a function of dilution ratio R (R=H2 /SiH4 ) at constant
pressure, assuming that all silicon atoms incident on the substrate contribute to growth regardless
of hydrogen coverage.
Figure 4.11 shows that the silicon to oxygen ratio decreases with temperature for temperatures
between 571 K and 711 K. This may explain the decrease in epitaxial thickness with temperature in
our experiments (Figure 4.9). At low temperature, the equilibrium surface coverage is high and the
fraction of empty sites at which oxidation can occur is low, while at high temperature, the initial
equilibrium surface coverage is low, which provides more empty sites for oxidation, although the
oxidation rate decreases slightly with temperature. At each temperature, there also appears to be
an optimal dilution at which the ratio of silicon to oxygen deposition is a maximum. At low dilution,
a monolayer of silicon is deposited more rapidly, but at the same time, there is less atomic hydrogen
to fill the empty sites on the surface. At high dilution, the empty sites are filled more quickly by
atomic hydrogen, but silicon deposition is slow, leading to a smaller silicon to oxygen ratio.
The model does not take into account gas-phase reactions in the chamber, nor does it include
the effects of etching. Including detailed gas phase reactions would likely decrease the flux of atomic
hydrogen, since atomic hydrogen may react with atomic hydrogen or SiHx to form H2 , and increase
the flux of Si by reacting with SiHx to form Si. This effect is similar to a decrease in dilution ratio
R and would shift the optimum dilution ratio to higher R. Including an etching mechanism would
decrease the flux of Si at high R. This effect would be similar to increasing R and the optimum
dilution ratio would shift to smaller R.
Although the model does not yet quantitatively predict the behavior of our reactor, it may
provide a qualitative insight into the data of Kitagawa et al. Based on the results of the model, it
is likely that at 430◦ C there does exist an optimal dilution at which the greatest epitaxial thickness
could be reached; it only lies beyond the limits of their experimental data. It is possible that the
maximum at 430◦ C may lie in the etching regime and thus can never be reached.
The dependence of the epitaxial thickness on the silicon to oxygen ratio is difficult to quantify.
However, it is known that, during MBE crystal growth, impurities at the growing interface can lead
to surface roughening and subsequent epitaxial breakdown through the formation of voids which may

Figure 4.11: Silicon to oxygen ratio in the first monolayer of growth as a function of dilution ratio
R (H2 /SiH4 at temperatures from 571 to 711 K. Pressure is held constant at 75 mTorr of a gas
mixture of H2 and 4% SiH4 in He.
lead to twinning and surface facets [99]. Although SIMS analysis performed by Evans Analytical,
seen in Figure 4.12, indicates that the oxygen content in our films is <1%, we have observed both the
formation of twin boundaries in our films and an increase in surface roughness with film thickness,
which point to oxygen incorporation as a possible contributory mechanism for epitaxial breakdown
in our films.
For our experiments, a decrease in the silicon to oxygen deposition ratio with temperature, as
predicted by the model, may explain the observed decrease in epitaxial thickness with temperature.
In addition, an increase in substrate temperature and corresponding decrease in hydrogen surface
coverage may lower adspecies diffusivity [100], promoting an earlier transition to polycrystalline
growth. Further dilution-dependent epitaxial growth experiments would be necessary to completely
develop a predictive model of epitaxial growth.

1E21

-3

Concentration (cm )

1E22

1E20

1E19

1E18
0.0

0.5

1.0

1.5

2.0

2.5

3.0

Depth (microns)

Figure 4.12: Carbon, hydrogen, and oxygen concentrations in 2.2 µm thick film grown at 300◦ C, as
determined by SIMS analysis.

4.4

Epitaxy on large-grained polycrystalline templates

4.4.1

Selective nucleation and solid phase epitaxy

Large-grained polycrystalline layers formed by the selective nucleation and solid-phase epitaxy
(SNSPE) process were used as templates for epitaxial growth. To fabricate SNSPE templates,
60 µL of a colloidal “ink” containing 20 µg nickel nanoparticles in 1 mL isopropanol was spun for
20 seconds at 1500 rpm onto a 1000 Åthick phosphorus-doped amorphous Si layer on SiO2 , leaving
a randomly distributed array of nanoparticles. During a subsequent vacuum anneal at 600◦ C, the
nanoparticles serve as heterogeneous nucleation sites for grain growth. The resulting polycrystalline
films have grain sizes on the order of 100 µm with low-angle grain boundaries. A schematic of
the SNSPE process is shown in Figure 4.13. More details can be found in reference [3]. Optical
micrographs of the crystallization process over a period of 10 hours are shown in Figure 4.14.

Ni particles

Nucleation sites are formed by
depositing Ni particles on Pimplanted a-Si layer.

a-Si
SiO2 substrate
Ni particles
c-Si
a-Si

Layer is annealed ~600°C to
nucleate and crystallize silicon.
Doping increases crystallization
rate.

Ni particles

Seeded grains impinge on each
other to form completely
crystallized film.

c-Si

Thick epitaxial layer is deposited
on templates by HWCVD; grain
size is that of the template layer.

c-Si

Figure 4.13: The SNSPE template fabrication process.

200 µm

1 hour

2 hours

4 hours

6 hours

8 hours

10 hours

Figure 4.14: Crystallization of SNSPE template layer [3]. The black dots are the nickel nanoparticles;
the white areas are grains of crystalline silicon and the grey areas are amorphous silicon regions.

Figure 4.15: Plan-view TEM of HWCVD epitaxial film (T=300◦ C) on SNSPE template. (a) Selected
area diffraction pattern from underlying SNSPE template. (b) Selected area diffraction pattern from
HWCVD film on SNSPE template. (c) Bright-field image indicating selected area diffraction regions.
Inset: diffraction from entire area.

4.4.2

Results

Silicon films 300 nm thick grown on SNSPE templates under the initial growth conditions were
investigated through plan-view TEM. The results, shown in Figures 4.15 and 4.16, are consistent
with low-temperature epitaxy on the scale of the 100-µm grains of the SNSPE templates. Epitaxial
breakdown is observed in the diffraction pattern of the HWCVD film, but some of the underlying
low-order diffraction spots are visible. The underlying film therefore likely has a morphology similar
to that of the HWCVD films on Si(100) [Figures 4.1 and 4.2]. The effect of the orientation of the
underlying grain structure of the SNSPE template on the morphology of the HWCVD film is shown
in Figure 4.16.
Cross-sectional analysis of these films reveals some areas of epitaxial growth as well as some areas
of columnar growth. Before HWCVD growth, the SNSPE templates were cleaned in a solution of
3:7 HNO3 :H2 O, which has been shown by Auger spectroscopy to remove elemental nickel from the
template surface[69]. The lack of epitaxy in some areas is thus more likely to have been caused
by the presence of ordinary surface contaminants, such as carbon and oxygen, than by the nickel
nanoparticles.
Cross-sectional analysis of 3.5 µm thick films grown on SNSPE templates under the revised
growth conditions also revealed some areas of epitaxy, as seen in Figure 4.17 (a) and (b). Because

Figure 4.16: (a) Bright-field image of HWCVD film (T=300◦ C) on SNSPE template showing selected
area diffraction regions. (b) Selected area diffraction from HWCVD film on (100)-oriented grain.
(c) Selected area diffraction from HWCVD film on a grain of different orientation.
the grains of the SNSPE template are large compared to the TEM viewing region and possess a high
intragranular defect density also observable in the films (Figure 4.17 (c) and (d)), it is difficult to
determine what constitutes a grain of the template. The diffraction pattern in the inset of Figure
4.17(a) was taken using a 0.5 µm selected area diffraction aperture, which allowed for diffraction
from the film, template layer, oxide, and a small region of the substrate. The high-intensity spotty
rings indicate large-grained polycrystalline growth in the first 100-150 nm of the film, which is also
consistent with some areas of epitaxy on the template grains. Further plan-view analysis, such
as orientation imaging microscopy, may be able to determine the size of regions which inherit the
orientation of the template grains.

4.5

Conclusions

Using TEM and RHEED, we have derived a phase diagram for HWCVD growth of Si on Si(100)
at temperatures between 300 and 475◦ C consisting of epitaxial, twinned epitaxial, mixed twinned
epitaxial/polycrystalline and polycrystalline phases in films between 50 nm and 2 µm thick. This
phase diagram can be understood within the context of a model in which a balance must be reached
between the thermal desorption rate of hydrogen from the surface and the adsorption and abstraction
rates of surface hydrogen by atomic hydrogen from the wire; this surface coverage limits the rate
of oxidation, which in turn affects the epitaxial thickness. This model can qualitatively explain

film
Si

SiO2

SNSPE

100 nm

500 nm

Figure 4.17: (a) Bright-field image of HWCVD film (T=300◦ C) on SNSPE template showing selected area diffraction region. Inset: selected area diffraction pattern showing areas of large-grained
polcrystalline growth. (b) Dark-field image corresponding to region in (a). (c) Bright-field image
of 3.5 µm thick film with high intragranular defect density. (d) Dark-field image corresponding to
region in (b).

45
the optimal dilution for the greatest epitaxial thickness at low temperature as well as the increase
in epitaxial thickness with dilution at high temperature. Results consistent with epitaxial growth
on large-grained SNSPE templates have also been presented, although further analysis, such as
orientation imaging microscopy, may be necessary to determine the size of regions which inherit the
orientation of the SNSPE template grains.

Chapter 5

Minority Carrier Lifetimes of
HWCVD Films
Abstract
We determine the minority carrier lifetimes of nearly-intrinsic films 1.5-15 µm thick grown by
HWCVD at 300◦ C on Si(100) and SNSPE templates through resonant-coupled photoconductive
decay (RCPCD) measurements. Although the microstructure of these films is mostly microcrystalline, the lifetimes for films on Si(100) range from 5.7 to 14.8 µs while those for films on SNSPE
templates range from 5.9 to 19.3 µs. Residual nickel present in the SNSPE templates does not significantly affect the lifetime of films grown on SNSPE templates, making the growth of epitaxial layers
by HWCVD on SNSPE templates a viable strategy for the fabrication of thin-film photovoltaics.
Ongoing work includes time-of-flight measurements of the minority-carrier mobility in these films.

5.1

Introduction

A requirement for the design of thin-film photovoltaics is that the minority carrier diffusion length
be greater than the thickness of the active layer. This diffusion length Ld is related to the minority
carrier lifetime τ such that Ld = Dτ , where D is the minority carrier diffusion coefficient in the
material. Another means of quantifying the electrical performance of photovoltaic materials is the
measurement of the mobility-lifetime product µτ , which for a given electric field E measures the
distance traveled by a free carrier before recombining (d = µτ E). Table 5.1 lists values of the
electrical properties of intrinsic films grown by HWCVD and PECVD on glass substrates (unless
listed otherwise) as reported in the literature.

47
Table 5.1: Reported electrical properties of intrinsic films.
Material
HWCVD a-Si

µτ
(cm2 /V)
10−7

Ld
(µm)

(cm2 /V·s)

(µs)

HWCVD a-Si on c-Si
HWCVD µc-Si
HWCVD µc-Si
HWCVD µc-Si
HWCVD µc-Si
PECVD µc-Si
PECVD µc-Si

10−7
10−8
5×10−7

0.334
1.2

2.8
10-15

16
.002-.003

5.2

Comments

Ref.

After light-induced
degradation
Surface-passivated
Hall mobility
Pulsed PECVD
VHF-PECVD

[101]
[102]
[103]
[104]
[105]
[106]
[107]
[108]

Recombination in semiconductors

We seek to measure a lifetime for minority carrier recombination in the HWCVD films. For a
p-type semiconductor in which we wish to investigate the behavior of the minority electrons, the
bulk recombination rate U for excess carriers ∆n and ∆p created by an excitation source can be
written [109]

U = A(n − n0 ) + B(pn − p0 n0 ) + Cp (p2 n − p0 2 n0 ) + Cn (pn2 − p0 n0 2 )

(5.1)

where n = n0 + ∆n and p = p0 + ∆p. Since in a p-type material n0
p0 , and if there is no trapping,
∆n = ∆p, we can simplify equation 5.1 as follows:

U = A∆n + B(p0 + n0 + ∆n)∆n + Cp (p0 2 + 2p0 ∆n + ∆n2 )∆n + Cn (n0 2 + 2n0 ∆n + ∆n2 )∆n. (5.2)
The recombination lifetime is then given by

τ=

∆n
= [A + B(p0 + n0 + ∆n) + Cp (p0 2 + 2p0 ∆n + ∆n2 ) + Cn (n0 2 + 2n0 ∆n + ∆n2 )]−1 . (5.3)

The second term in equation 5.3 represents band to band radiative recombination, for which the
lifetime is inversely proportional to the carrier concentration because both electrons and holes must
be present for recombination to occur. Since silicon has an indirect bandgap, radiative recombination
is weak. The third and fourth terms represent Auger recombination, a three-carrier process for which
the lifetime is inversely proportional to the square of the carrier concentration. It becomes significant
only when either the majority carrier or excess minority carrier concentration is very high.

48
The first term in equation 5.3 represents Shockley-Read-Hall (SRH) recombination[109, 110],
which takes place through a two-step transition through a deep level recombination center in the
middle of the band gap. This mechanism is always active since there are always impurities or defects
in semiconductor materials. For a material with an impurity concentration NT of energy level ET ,
the SRH lifetime is

τSRH =

τp (n0 + n1 + ∆n) + τn (p0 + p1 + ∆n)
p0 + n0 + ∆n

(5.4)

where τn and τp are the electron and hole lifetimes, respectively. These can be written in terms of the
defect concentration, the thermal carrier velocity and the electron and hole capture cross-sections:

τn =

σn vth Nt

(5.5)

τp =

σp vth Nt

(5.6)

n1 and p1 are defined as

n1 = ni exp
and

ET − Ei
kT

ET − Ei
p1 = ni exp −
kT

(5.7)

(5.8)

Low-level injection (LLI) conditions are present when the excess minority carrier concentration is
small compared to the equilibrium majority carrier concentration, ∆n
p0 . The lifetime τSRH = τn
in this case. Under high-level injection (HLI) conditions, ∆n
p0 and the lifetime τSRH = τn + τp .

5.3

Resonant-coupled photoconductive decay

The resonant-coupled photoconductive decay (RCPCD) technique is a contactless method for measuring minority carrier lifetime developed by Richard Ahrenkiel and Stephen Johnston of NREL in
1998[111]. In this technique, the sample is placed on a movable insulating platform which is positioned at variable distances from a small antenna such that the sample becomes part of a coupled
antenna array. The antenna is part of a high-Q tuned circuit, and when the sample is placed near
the antenna, the mutual impedance modifies the input impedance of the antenna. This assembly is
placed at the center of a highly conducting box reflector. The entire apparatus is enclosed in a larger
enclosure that is a resonant cavity at the resonance frequency of the sensor such that the walls of
the enclosure become nodes of the rf standing waves and the sample lies at an antinode. Figure 5.1
shows a schematic of the apparatus.

49
A microwave generator in the 400–900 MHz range is used as a probe; the resulting electromagnetic waves are reflected by free carriers in the semiconductor sample. The sample absorbs and
reradiates these primary electromagnetic waves in phase with the driving antenna. The intensity of
the reradiated electromagnetic waves depends on the carrier concentration in the sample. A pulsed
light source is then used to generate excess carriers, which change the reflection coefficient of the
microwave signal. The driving antenna then absorbs the photogenerated electromagnetic waves and
transfers the energy into an ac voltage, which is recorded on a digital oscilloscope. This corresponds
to the decay in the free carrier concentration in the sample such that

∆s (t)
V (t) = AZ12

(5.9)

where A is the system gain, Z12 is the mutual impedance between the sample and antenna, and
∆s (t) is the transient photoconductivity of the sample. When recombination can be written in terms
of a single lifetime, the change in photoconductivity is given by

∆σ = q(µn + µp )∆n exp(−t/τ )

(5.10)

where τ is the minority carrier lifetime.
The surface recombination velocity S at unpassivated surfaces is also an important consideration.
The effective lifetime measured by RCPCD is given by[112]
τef f

τSRH

(5.11)

where d is the sample thickness. The surface recombination velocity is generally unknown and so
the lifetime measured by RCPCD is a lower bound on the true lifetime in the material.

5.4

Experiment

HWCVD films of 1.5, 3.5, 11.5 and 15 µm thicknesses were grown at 300◦ C on Si(100) and SNSPE
templates. Growth of a given film thickness on Si(100) and SNSPE templates was performed in
the same experiment. The Si(100) substrates were p-type with resistivity 100 Ω·cm; the SNSPE
templates were degenerately doped n-type (n=1020 ). Films were nearly intrinsic (p=1012 ) as determined by spreading resistance analysis (performed by Solecon Labs). As we saw in Chapter 4,
epitaxial growth at 300◦ C persists to a thickness of between 1 and 2 µm, so the microstructure of
thick films was primarily microcrystalline.
A lower wire temperature of 1750◦ C was used to minimize W incorporation into the films. SIMS
analysis performed by Evans Analytical Group, seen in Figure 5.2, showed bulk W levels of <1×1017
in films grown at 1800◦ C and <1×1016 in films grown at 1750◦ C. (In each case, the W concentration

hν

sample
platform

antenna
directional reflector
high-Q resonant circuit

oscilloscope
Figure 5.1: Basic schematic of the RCPCD apparatus.
at the surface was an order of magnitude higher than that in the bulk, since exposure to the W wire
was necessary to heat the sample to 300◦ C.)
The minority carrier lifetimes of these films were measured by RCPCD, using a 532 nm laser
as the excitation source. The lowest possible excitation power was used and was too low to be
measured; an upper limit on the power is 1 µW which corresponds to approximately 1/10 mJ per
10 ms pulse in a 5 mm spot size. Based on these estimates we can estimate an upper bound on ∆p
of approximately 1×1015 cm−2 . No effort was made to passivate the film surfaces.
The absorption coefficient of Si at 532 nm is approximately 9×10−3 cm−1 , which gives a penetration depth of approximately 1.1 µm [113], so we can be sure that carrier generation occurs in
the films and not in the Si(100) substrate. The lifetime of a Si(100) wafer with no film was also
measured for comparison. Because the SNSPE templates are only 100 nm thick, the lifetime of the
template layer alone cannot be reliably measured by RCPCD at 532 nm.

1E19

1800 C
1750 C

-3
W concentration (cm )

1E18

1E17

1E16

1E15

1E14

1E13
0.0

0.5

1.0

1.5

2.0

2.5

3.0

Depth (microns)

Figure 5.2: W concentration, as determined by SIMS analysis, in 300◦ C HWCVD silicon films grown
on Si(100) at wire temperatures of 1800◦ C and 1750◦ C. The higher W concentration at the surface
of both films is due to exposure to the W wire before growth, which was necessary to heat the
samples to 300◦ C.

5.5

Results

The RCPCD voltage signal as a function of time for each film can be found in Figures 5.3 and 5.4.
One or more exponential decays were fit to the curves from which the minority carrier lifetimes for
each sample under HLI and LLI conditions were derived. The measured minority carrier lifetime is
actually an effective lifetime; because the surface recombination velocity is not known, this effective
lifetime is a lower bound on the true minority carrier lifetime in the material. The curvature of the
data indicates the dominant type of recombination center in each film.
In Figure 5.3(a), the RCPCD data for a 1.5 µm HWCVD film on Si is typical of that for bulk
Si, with the HLI lifetime greater than the LLI lifetime. This is consistent with an epitaxial film on
Si(100). Under illumination, the charged midgap recombination centers fill up quickly and the rest
of the excess carriers fill neutral centers, so that under HLI conditions the dominant process is hole

NREL ELECTROOPTICAL CHARACTERIZATION GROUP

10.82
Lifetime (us)

102 Tau(us)

7.176

101

Sample #
Todays date
Meas Date

CT_A_SIG532A
5-Jan-4
12/11/03_
1:09 PM;
30
t (microseconds)

14.74

Sample #
Todays date
Meas Date

10 3

14.79

NREL ELECTROOPTICAL CHARACTERIZATION GROUP
RF CONDUCTIVITY LIFETIME

10 2 Tau(us)

CT_B_SIG532A
5-Jan-4
12/11/03_
1:12 PM;
20
25
30
t (microseconds)

5.693

V (mV)

102 Tau(us)

7.506
Lifetime (us)

RF CONDUCTIVITY LIFETIME

101

NREL ELECTROOPTICAL CHARACTERIZATION GROUP

103

RF CONDUCTIVITY LIFETIME

V (mV)

102 Tau(us)

NREL ELECTROOPTICAL CHARACTERIZATION GROUP

103

RF CONDUCTIVITY LIFETIME

V (mV)

103

101

10 1

Sample #
Todays date
Meas Date

CT_C_SIG532A
5-Jan-4
12/11/03_
1:05 PM;
30
t (microseconds)

Sample #
Todays date
Meas Date

CT_D_SIG532A
11-Dec-3
12/11/03_
1:15 PM;

15
20
25
t (microseconds)

Figure 5.3: RCPCD voltage vs. time curves for HWCVD films of various thicknesses on Si(100).
(a) 1.5 µm, (b) 3.5 µm, (c) 11.5 µm, (d) 15 µm. Straight lines indicate exponential decay fits to the
data.
capture, which is slower than electron capture. The LLI lifetime then reflects the release of carriers
from the midgap recombination centers in the material [114].
In 3.5 µm and 11.5µm thick films on Si(100) (Figure 5.3 (b) and (c)), the HLI lifetime is lower
than the LLI lifetime. Such a decay pattern is indicative of a shallow recombination center[114].
Since the microstructure of these thicker films is mostly polycrystalline, hydrogen-passivated grain
boundaries may be responsible. For a 15 µm thick film on Si(100) (Figure 5.3(d)), a single decay is
observed, corresponding to the LLI lifetime.
The decay patterns of HWCVD films on SNSPE templates, seen in Figure 5.4, have a fast
component at the beginning of the illumination. This is likely due to a surface roughness effect;
for samples with very rough surfaces, the surface recombination velocity component of the minority
carrier lifetime is dominant in the early stages of illumination before the carriers diffuse into the bulk.
This feature is less pronounced for the thicker films, which may indicate a decrease in roughness
with film thickness.
The decay for the 1.5 µm thick film (Figure 5.4 (a)) indicates a single lifetime, while the decays for
3.5µm and 11.5µm thick films (Figure 5.4 (b) and (c))are characteristic of a deep-level recombination

53
NREL ELECTROOPTICAL CHARACTERIZATION GROUP

V (mV)

Tau(us)

19.16
Lifetime (us)

102 Tau(us)

1.211

Sample #
Todays date
Meas Date

10 2

RF CONDUCTIVITY LIFETIME

Sample #
Todays date
Meas Date

10.86
Lifetime (us) 2

CT_G_SIG532A
5-Jan-4
12/11/03_
1:29 PM;

15
20
25
t (microseconds)

CT_F_SIG532A
5-Jan-4
12/11/03_
1:26 PM;
35

RF CONDUCTIVITY LIFETIME

Tau(us)

Sample #
Todays date
Meas Date

7.465

NREL ELECTROOPTICAL CHARACTERIZATION GROUP

12.92

5.936
V (mV)

20
25
30
t (microseconds)

Tau(us)

100

14.74
Lifetime (us)

100

NREL ELECTROOPTICAL CHARACTERIZATION GROUP

V (mV)

CT_E_SIG532A
5-Jan-4
12/11/03_
1:20 PM;

15
20
25
t (microseconds)

101

RF CONDUCTIVITY LIFETIME

102

NREL ELECTROOPTICAL CHARACTERIZATION GROUP

103

RF CONDUCTIVITY LIFETIME

V (mV)

103

10 0

Sample #
Todays date
Meas Date

CT_H_SIG532A
11-Dec-3
12/11/03_
1:34 PM;

15
20
25
t (microseconds)

Figure 5.4: RCPCD voltage vs time curves for HWCVD films of various thicknesses on SNSPE
templates. (a) 1.5 µm, (b) 3.5 µm, (c) 11.5 µm, (d) 15 µm. Straight lines indicate exponential decay
fits to the data.
center. This center may arise from the diffusion of residual nickel from the SNSPE templates into
the films. The 15 µm thick film on SNSPE templates is also characterized by a single lifetime. The
factor of two discrepancy in lifetime values may be due to nonuniformity in the films, i.e., it may
depend on whether a “good” or “bad” region of each film was illuminated. Although nickel is a
known lifetime killer even in small concentrations [115], the lifetimes of films on SNSPE templates
are comparable to the lifetimes of films on Si(100).
The minority carrier results are summarized in Figures 5.5 and 5.6 for films on Si(100) and
SNSPE templates, respectively. Under LLI conditions, the minority carrier lifetimes for films on
Si(100) range from 5.7 to 7.5 µs, and the minority carrier lifetimes for films on SNSPE templates
range from 5.9 to 19.3 µs.
Polycrystalline films grown by HWCVD have been used in the fabrication of 1.5 µm-thick thinfilm transistors with channel mobilities of 4.7 cm2 /V·s on glass substrates [116]. Using the Einstein
relation, we can determine that, if the mobilities in our films were comparable, the minority carrier
diffusion coefficient would be 0.1175 cm2 /s. From this value and the minority carrier lifetime of ∼7
µs measured by RCPCD in a 1.5 µm thick film on Si(100), we obtain a value for the minority carrier

Bulk Si(100) LLI

Minority carrier lifetime (µs)

LLI
HLI

16
14
12
10

Bulk Si(100) HLI

Film thickness (µm)

Figure 5.5: LLI and HLI minority carrier lifetimes of HWCVD films on Si(100) as measured by
RCPCD. The dashed and dotted lines represent the LLI and HLI lifetimes, respectively, of the bulk
Si(100) substrate.
diffusion length of approximately 9 µm, which is comparable to the thicknesses of the active layers
for thin-film photovoltaics (1–30 µm). The minority carrier lifetimes of films on SNSPE templates
are comparable, making it possible that the growth of epitaxial films by HWCVD on large-grained
SNSPE templates is a viable strategy for the fabrication of thin-film photovoltaics.

5.6

Conclusions

The minority carrier lifetimes of nearly-intrinsic epitaxial/microcrystalline films grown on Si(100)
by HWCVD range from 5.7 to 7.5 µs. The lifetimes of films grown under the same conditions on
SNSPE templates range from 5.9 to 19.3 µs, making them suitable for incorporation into photovoltaic
devices. In particular, residual nickel from the SNSPE templates does not appear to be significantly
detrimental to the lifetime of films grown on these templates. If the mobilities in these films are

LLI
HLI

Minority carrier lifetime (µs)

18
16
14
12
10

Film thickness (µm)

Figure 5.6: LLI and HLI minority carrier lifetimes of HWCVD films on SNSPE templates as measured by RCPCD.
also high, it is possible that HWCVD epitaxy on large-grained SNSPE templates could be a viable
strategy for the fabrication of thin-film photovoltaics.
The mobility is an important factor in the determination of material quality for the i-layers of
photovoltaic devices. Many experimental data suggest that improvements in the µτ product come
from improvements in the mobility [106]. Ongoing work involves time-of-flight measurements of the
mobilities in identical films on Si(100) and SNSPE templates to be performed by Eric Schiff and
Steluta Dinca at Syracuse University.

Chapter 6

Conclusions and Future Work
We have explored the viability of two strategies for the growth of large-grained polycrystalline films
on glass substrates for thin-film photovoltaic applications. First, we consider direct growth on SiO2 .
Here, an increase in grain size of continuous polycrystalline silicon films with hydrogen dilution can
be attributed to atomic hydrogen etching of silicon monomers, decreasing the nucleation density. Experiments show that the nucleation density increases sublinearly with time at low coverage, implying
a fast nucleation rate until a critical density is reached, after which grain growth begins. Through
temperature-dependent nucleation-density measurements, the activation energy for diffusion of Si
monomers on SiO2 during HWCVD growth is estimated to be 0.47±0.09 eV. To our knowledge, this
is the first estimate for this activation energy given in the literature.
The experimental nucleation density measurements can be understood within the framework of
a rate-equation pair-binding simulation. Modelling of the temperature-dependent cluster density
measurements give D0 =0.1±0.03 cm2 /s and Ea =0.42±0.01 eV, which is within the error in the
experimentally determined value. Monomer etching by atomic hydrogen is simulated by changing
the adatom stay time τa , and the simulated etch rates vary approximately linearly with H2 dilution.
The model can also be used to explore possible strategies for the rapid growth of large-grained
polycrystalline films by HWCVD.
The second strategy involves the use of large-grained polycrystalline layers fabricated on SiO2
by selective nucleation and solid-phase epitaxy as templates for epitaxial growth by HWCVD. Using TEM and RHEED, we have derived a phase diagram for HWCVD growth of Si on Si(100) at
temperatures between 300–475◦ C consisting of epitaxial, twinned epitaxial, mixed twinned epitaxial/polycrystalline and polycrystalline phases in films between 50 nm and 2 µm thick. This phase
diagram can be understood within the context of a model in which a balance must be reached between the thermal desorption rate of hydrogen from the surface and the adsorption and abstraction
rates of surface hydrogen by atomic hydrogen from the wire; this surface coverage limits the rate
of oxidation, which in turn affects the epitaxial thickness. This model can qualitatively explain the
optimal dilution for the greatest epitaxial thickness at low temperature as well as the increase in

57
epitaxial thickness with dilution at high temperature, although dilution-dependent epitaxial growth
experiments must be performed in order to completely develop a truly predictive model for epitaxial
growth. Results consistent with epitaxial growth on large-grained SNSPE templates have also been
presented, although further analysis, such as orientation imaging microscopy, may be necessary to
determine the size of regions which inherit the orientation of the SNSPE template grains.
The minority carrier lifetimes of nearly-intrinsic epitaxial/microcrystalline films grown on Si(100)
by HWCVD range from 5.7 to 14.8 µm. The lifetimes of films grown under the same conditions
on SNSPE templates range from 5.9 to 19.3 µs, making them suitable for incorporation into photovoltaic devices. In particular, nickel from the SNSPE templates does not appear to be significantly
detrimental to the lifetime of films grown on these templates. If the mobilities in these films are
also high, it is possible that HWCVD epitaxy on large-grained SNSPE templates could be a viable
strategy for the fabrication of thin-film photovoltaics.
Ongoing work involves time-of-flight measurements of the mobilities in identical films on Si(100)
and SNSPE templates to be performed by Eric Schiff and Steluta Dinca at Syracuse University.
Since the high degree of grain-boundary passivation is thought to enhance the electrical properties of
HWCVD films, further experiments may determine a correlation between the lifetimes and mobilities
of HWCVD films and grain boundary hydrogen content as determined by fourier-transform infrared
spectroscopy (FTIR). The incorporation of these layers into photovoltaic devices is, of course, the
ultimate goal.

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Appendix A

The HWCVD Reactor
This appendix gives further details of the design and construction of the HWCVD reactor used in
our experiments.
A detailed diagram of the HWCVD reactor can be seen in Figure A.1, and photographs of the
reactor from two different angles can be seen in Figure A.2. The precursor gases (1–4% SiH4 in He
and H2 ) are introduced through separate mass flow controllers and mix in a short length of 0.25
inch stainless steel tubing before entering the chamber. The gas pressures are measured with a
capacitance manometer which functions in the range from 1 mTorr to 20 Torr. The gas pressures
can be varied by controlling the effective pumping speed with a butterfly valve (later replaced by a
manual gate valve) at the bottom of the chamber. An ionization gauge measures the base pressure
of the chamber, which is typically on the order of 10−7 Torr.
For growth over a small sample area, a single tungsten wire is resistively heated with a DC power
supply capable of 30 V and 25 A. A tungsten wire of 0.5 mm diameter reaches a temperature of
1850◦ C at approximately 8 V and 16 A. Large area growth is also possible with a wire array [117].
A linear feedthrough allows precise control of the distance from the wire to the substrate. This
feedthrough is not normally mounted on the port where it is shown in Figure A.2 (b), but is located
directly opposite the substrate heater, as indicated in Figure A.1.
Figure A.3 shows a top view of the inside of the HWCVD reactor, with the wire and substrate
heater visible. The wire is supported by a stainless steel bracket and separated from the bracket by
ceramic standoffs. Since copper wire can be corroded by silane, power is delivered through stainless
steel wires encased in ceramic beads and terminated in stainless steel compression sleeves which
attach to a small set screw around which the wire is wound. A second set of ceramic standoffs are
used to keep the wire and power leads in place.
The substrate heater uses a tungsten ribbon filament and is capable of delivering substrate
temperatures of up to 500◦ C. The sample block attaches to the outer ring through a locking pin
mechanism. The gear assembly seen in Figure A.3 enables 360 degree rotation of the outer ring
and sample block while the heater itself remains stationary. The translatable shutter described in

dotted line = above plane
dashed line = below plane
pressure transducer:
1-760 mTorr

resistive substrate heater or
HIDEN differentially-pumped
quadrupole mass spectrometer
(250 L/s turbopump)

RHEED
gun

top flange with
viewport
gas inlet

shutter arm

Inficon
quartz crystal
deposition
monitor
RHEED screen

main chamber
pumping - 330 L/s
turbopump

ion gauge

wire traverse
Figure A.1: Schematic of the HWCVD reactor.
Chapter 3 is a thin tantalum plate attached to the load lock transfer arm. Figure A.4 illustrates the
wire, substrate and shutter geometry used for all growth experiments.
In principle, with the use of a bellows, the position of the heater can also be translated with
respect to the wire. This would enable transfer of samples into the chamber using the load lock and
transfer arm; in our experiments, the sample block was manually placed onto the heater assembly
through the top viewport. Lateral translation of the heater would also enable in situ RHEED
measurements using the electron gun visible in Figures A.1 and A.2, as this translation is necessary
to properly align the sample with the electron beam.

capacitance
manometer

top viewport

wire DC power
supply

RHEED
gun
main vacuum
chamber

gate valve

mass flow controllers

ion gauge

load lock

RHEED
gun
top viewport
wire DC power
supply

gas inlet

capacitance
manometer

wire linear
motion
feedthrough

load lock

chamber
butterfly
valve

substrate heater

mass flow
controller

Figure A.2: Photographs of the HWCVD reactor. (a) Front view. (b) Side view.

wire
supporting
assembly

chamber
butterfly
valve
substrate
heater

ceramic
standoffs

DC power
leads

ion gauge

Figure A.3: Top view of the inside of the HWCVD reactor. The wire is on and is normal to the
plane of the photograph.

sample holder
2” dia.

shutter translation

sample ~ 2” x 0.5”

wire: 12 cm length
Figure A.4: Schematic of the inside of the HWCVD reactor during growth experiments.

Appendix B

Nucleation Model Code
The following MATLAB functions were used for the nucleation model in Chapter 3.
Function “mysimB” is the main program for solving the system of coupled differential equations.
It calls function “myodeB” which finds the time derivative of the system state given by the number
of monomers n1 , critical clusters nx and fractional surface coverage Z. By guessing values for D0
and Ea and plotting the results against the data the best fit for the family of curves can be found.
Relative stay times under various etching conditions can be found by changing the value of τa and
looking for the best fit to the data.

global R ta tn k T D sigma_x Na N0 C_i beta E_i sigma_i i;

bj_values = [0 1 3 5 7 9 12 14 16 18];
C_values = [1 3 2 3 6 6 1];

i=1;
%R=6*10^13; too high
R=5*10^(10);
ta=2.5e-5;
% tn = 3.9486*10^(-8); eliminate this term from model
k = 8.62*10^(-5); %ev/K boltzmann constant
T = 573;% T in K
D0 = 1*10^(-1); %diffusion prefactor Si on Si = 10^(-3)
D = D0*exp(-0.42/(k*T)); %diffusion constant
sigma_x = 5;
sigma_i = 2;
Na = 10^15;
N0 = 10^15;
B_i = bj_values(i);
E_b = 1.55; %ev bond energy

if i<8
C_i = C_values(i);
else
C_i = 1;

% don’t know what C_i should be for high values of i

end;

E_i = B_i*E_b;
beta = 1/(k*T);
gamma_i = C_i*(N0^(1-i))*exp(beta*E_i);

ta2 = 10^(4);

% time for a 2-cluster to break apart

[t,state]=ode23t(’myodeB’,[0 10000],[0 0 0 0]’);

n1 = state(:,1);
nx = state(:,2);
Z = state(:,3);

70
nxwx = state(:,4);

figure(1);
plot(t,n1);
xlabel(’t’);
ylabel(’n_1’);

figure(2);
plot(t,nx);
xlabel(’t’);
ylabel(’n_x’);

figure(3);
plot(t,Z);
xlabel(’t’);
ylabel(’Z’);

figure(4);
plot(t,nxwx);
xlabel(’t’);
ylabel(’nxwx’);

function [dstate] = myode(t,state);

global R ta tn D sigma_x Na N0 C_i beta k T E_i sigma_i i;

%if t < 200
ta = 2.5e-5;
%elseif t > 250
%ta = 2500;
%else
%ta = (2.5e-5) + (2500 - 2.5e-5)*(t - 200)/50;
%end;

n1 = state(1);

nx = state(2);

Z = state(3);

nxwx = state(4);

Z = min(Z,1);

% can’t have Z>1

dnxwxdt = (n1.*sigma_i.*D.*n1) + (n1.*sigma_x.*D.*nx) + R.*Z;

dn1dt = R - n1./ta - 2.*(n1.*sigma_i.*D.*n1) - (n1.*sigma_x.*D.*nx) - (R.*Z);

dZdt = (1./Na) .* dnxwxdt;

dnxdt = (n1.*sigma_i.*D.*n1) - 2.*nx.*dZdt;

dstate = [dn1dt dnxdt dZdt dnxwxdt]’;

Appendix C

Hydrogen Surface Coverage Model
Code
The following Mathematica function was used to model the hydrogen surface coverage under HWCVD
conditions using the equations in Chapter 4. It finds the equilibrium surface coverage under HWCVD
conditions considering absorption, abstraction and thermal desorption rates, and determines the number of
oxygen atoms per monolayer of silicon deposition by starting the hydrogen coverage at its equilibrium value
when no hydrogen flux is present and finding the subsequent surface coverage, silicon deposited and oxygen
deposited as a function of time.

73
Tsub = 711;
Twire = 2073;
theta0 = 0.3744;

R = 70;

Ptot = 75 * 10^(-3);

PSiH4 = Ptot / (R+25);

PSiH4inHe = 25 * PSiH4;

PHe = PSiH4 * 24;

PH2 = Ptot - PSiH4inHe;

O2flux = 2.558 * 10^(13) * N[Sqrt[573/Tsub]];

NN = 6.8*10^14;

PstickH = 0.6 * Exp[-6.94 * 10^(-22) / (k * Tsub)];
Pabs = 0.52 * Exp [-1.39 * 10^(-20) / (k * Tsub)];
PstickO = 0.01;

h = 6.626 * 10^(-34);
c = 3 * 10^10;
k = 1.38 * 10^(-23);
epsilon1 = 6.0 * 4184 / (6.022 * 10^23);
epsilon2 = 19 * 4184 / (6.022 * 10^23);
nua = 2 * 10^(15);
Ea = 57.2 * 4184 / (6.022 * 10^23);
nub = 3.2 * 10^(13);
Eb = 43 * 4184 / (6.022 * 10^23);

mh = 1.7 * 10^(-27);
dh = 1.06 * 10^(-10);
dHe = 0.62 * 10^(-10);
mHe = 4 * 1.7 * 10^(-27);

74
dsi = 2.2 * 10^(-10);

rwire = .025;
dwsub = 2.5;

Fluxatwire = (PH2 * 133 * 0.14) / (100^2 * Sqrt [2 * Pi * mh * k * Twire]);

Fluxnocoll = Fluxatwire * rwire / dwsub;

fluxin = Fluxnocoll;

FluxSiH4wire = (PSiH4 * 133 * 0.7) / (100^2 * Sqrt [2 * Pi * 28 * mh * k *
Twire]);

FluxncSiH4 = FluxSiH4wire * rwire / dwsub;

fluxinSi = FluxncSiH4;

Fluxratio = (fluxin + fluxinSi) / fluxinSi;

T = Tsub;

Print["T = ",Tsub];
Print["Ptot = ",Ptot];
Print["R = ",R];
Print["PSiH4 in He = ",PSiH4inHe];
Print["PSiH4 = ",PSiH4];
Print["PH2 = ",PH2];
Print["fluxin = ", fluxin];
Print["flux silicon in = ",fluxinSi];

Print["flux ratio = ", Fluxratio];

Q10 = Exp[-h*c*(2093)/2/k/T] * Exp[-h*c*(621)/2/k/T] / (1 - Exp[-h*c*(2093)/k/T]
) / (1 - Exp[-h*c*(621)/k/T]);
Q11 = Exp[-h*c*(2088)/2/k/T] * Exp[-h*c*(2099)/2/k/T] / (1 - Exp[-h*c*(2088)/k/T
]) / (1 - Exp[-h*c* (2099)/k/T]);
Q2

= Exp[-h*c*(637)/2/k/T] * Exp[-h*c*(2091)/2/k/T] * \
Exp[-h*c*(2104)/2/k/T] * Exp[-h*c*(910)/2/k/T] / (1 - Exp[-h*c*(637)/k/T])

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/ (1 - Exp[-h*c*(2091)/k/T]) / (1 - Exp[-h*c*(2104)/k/T]) / (1 - Exp[-h*c* (910
)/k/T]);

VerboseDthetadt[Theta_] :=Module[{theta00,theta10,theta11,theta2,eqn3,sol3,theta
11A,theta11B,eqn4,eqn4A,eqn4B,sol4A,sol4B,sols,solns,realsolns,n,t10,t11,t00,t2,
dThetadtdes,dThetadtads,dThetadtabs,dThetadt},
theta00 = 1 - theta10 - theta11 - theta2;
theta10 = 2 (Theta - theta11 - 2 theta2);
eqn3 = {theta10^2 / theta00 / theta11 == 4 Q10^2 / \
Q11 * Exp[-epsilon1/k/T]};
sol3 = Solve[eqn3,theta11];
theta11A = Expand[theta11 /. sol3[[1]]];
theta11B = Expand[theta11 /. sol3[[2]]];
eqn4 = {theta10^2 theta2^2 / theta11^3 / (1 + theta2) == \
Q10^2 Q2^2 / Q11^3 Exp[- 2 epsilon2 / (2 k T)]};
eqn4A = eqn4 /. {theta11 -> theta11A};
eqn4B = eqn4 /. {theta11 -> theta11B};
sol4A = Solve[eqn4A,theta2];
sol4B = Solve[eqn4B,theta2];
sols={};
For[n=1, n<=Length[sol4A], n++,sols= Append[sols, Union[sol3[[1]] /. sol4A[[n]],
sol4A[[n]]]]];
For[n=1, n<=Length[sol4B], n++,sols= Append[sols, Union[sol3[[2]] /. sol4B[[n]],
sol4B[[n]]]]];
solns = {theta00, theta10, theta11, theta2} /. sols;
realsolns = solns;
realsolns = Select[realsolns, Im[#[[1]]]==0 & ];
realsolns = Select[realsolns, Im[#[[2]]]==0 & ];
realsolns = Select[realsolns, Im[#[[3]]]==0 & ];
realsolns = Select[realsolns, Im[#[[4]]]==0 & ];
realsolns = Select[realsolns, Re[#[[1]]]>0 & ];
realsolns = Select[realsolns, Re[#[[2]]]>0 & ];
realsolns = Select[realsolns, Re[#[[3]]]>0 & ];
realsolns = Select[realsolns, Re[#[[4]]]>0 & ];
Print["Theta = ",Theta];
Print[realsolns];
If[Length[realsolns]>0,
t00 = realsolns[[1]][[1]];

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t10 = realsolns[[1]][[2]];
t11 = realsolns[[1]][[3]];
t2 = realsolns[[1]][[4]];
dThetadtdes = (-nua*t11*Exp[-Ea/k/T] - nub*t2^2*Exp[-Eb/k/T]);
Print["dTheta/dt (desorption) = ",dThetadtdes];
dThetadtads = fluxin * PstickH * (2 - Theta) / 2 / NN;
Print["dTheta/dt (adsorption) = ",dThetadtads];
dThetadtabs = - fluxin * Pabs * (Theta) / 2 / NN;
Print["dTheta/dt (abstraction) = ",dThetadtabs];
dThetadt = dThetadtdes + dThetadtads + dThetadtabs;
Print["dTheta/dt = ",dThetadt];
dThetadt,0]];

Dthetadt[Theta_] :=Module[{theta00,theta10,theta11,theta2,eqn3,sol3,theta11A,the
ta11B,eqn4,eqn4A,eqn4B,sol4A,sol4B,sols,solns,realsolns,n,t10,t11,t00,t2,dThetad
tdes,dThetadtads,dThetadtabs,dThetadt},
theta00 = 1 - theta10 - theta11 - theta2;
theta10 = 2 (Theta - theta11 - 2 theta2);
eqn3 = {theta10^2 / theta00 / theta11 == 4 Q10^2 / \
Q11 * Exp[-epsilon1/k/T]};
sol3 = Solve[eqn3,theta11];
theta11A = Expand[theta11 /. sol3[[1]]];
theta11B = Expand[theta11 /. sol3[[2]]];
eqn4 = {theta10^2 theta2^2 / theta11^3 / (1 + theta2) == \
Q10^2 Q2^2 / Q11^3 Exp[- 2 epsilon2 / (2 k T)]};
eqn4A = eqn4 /. {theta11 -> theta11A};
eqn4B = eqn4 /. {theta11 -> theta11B};
sol4A = Solve[eqn4A,theta2];
sol4B = Solve[eqn4B,theta2];
sols={};
For[n=1, n<=Length[sol4A], n++,sols= Append[sols, Union[sol3[[1]] /. sol4A[[n]],
sol4A[[n]]]]];
For[n=1, n<=Length[sol4B], n++,sols= Append[sols, Union[sol3[[2]] /. sol4B[[n]],
sol4B[[n]]]]];
solns = {theta00, theta10, theta11, theta2} /. sols;
realsolns = solns;
realsolns = Select[realsolns, Im[#[[1]]]==0 & ];
realsolns = Select[realsolns, Im[#[[2]]]==0 & ];
realsolns = Select[realsolns, Im[#[[3]]]==0 & ];

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realsolns = Select[realsolns, Im[#[[4]]]==0 & ];
realsolns = Select[realsolns, Re[#[[1]]]>0 & ];
realsolns = Select[realsolns, Re[#[[2]]]>0 & ];
realsolns = Select[realsolns, Re[#[[3]]]>0 & ];
realsolns = Select[realsolns, Re[#[[4]]]>0 & ];
If[Length[realsolns]>0,
t00 = realsolns[[1]][[1]];
t10 = realsolns[[1]][[2]];
t11 = realsolns[[1]][[3]];
t2 = realsolns[[1]][[4]];
dThetadtdes = (-nua*t11*Exp[-Ea/k/T] - nub*t2^2*Exp[-Eb/k/T]);
dThetadtads = fluxin * PstickH * (2 - Theta) / 2 / NN;
dThetadtabs = - fluxin * Pabs * (Theta) / 2 / NN;
dThetadt = dThetadtdes + dThetadtads + dThetadtabs;
dThetadt = N[dThetadt];
ClearAll[theta00,theta10,theta11,theta2];
dThetadt,0]];

ClearAll[theta];
theta = theta0;
Odeposit = 0;
Sideposit = 0;
stepsize = 0.002;
dthdt = 9999;
n = 0;
While[Sideposit<6.8*10^14,
t = n*stepsize;
Print["t = ",n*stepsize];
Print["theta = ",theta];
Print["deposited Oxygen atoms = ",Odeposit];
Print["deposited Silicon atoms = ",Sideposit];
If[Abs[dthdt]>10^(-7),dthdt = Dthetadt[theta],dthdt=0];
Print["Dtheta/Dt = ",dthdt];
Print[];
theta = theta + dthdt * stepsize;
Odeposit = Odeposit + O2flux * (2 - theta) * PstickO * stepsize;
Sideposit = Sideposit + fluxinSi * stepsize;
n=n+1];